Advertisement
| a mathematical introduction to logic: A Mathematical Introduction to Logic Herbert B. Enderton, 2001-01-23 A Mathematical Introduction to Logic |
| a mathematical introduction to logic: A Mathematical Introduction to Logic Herbert B. Enderton, 1972-06-16 This book gives a mathematical treatment of the basic ideas and results of logic. It is intended to serve as a textbook for an introductory mathematics course in logic at the junior-senior level. The objectives are to present the important concepts and theorems of logic and to explain their significance and their relationship to the reader's other mathematical work. |
| a mathematical introduction to logic: An Introduction to Mathematical Logic Richard E. Hodel, 2013-01-01 This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition. |
| a mathematical introduction to logic: A Friendly Introduction to Mathematical Logic Christopher C. Leary, Lars Kristiansen, 2015 At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises. |
| a mathematical introduction to logic: Introduction to Mathematical Logic Elliot Mendelsohn, 2012-12-06 This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from Cantor's paradise (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees. |
| a mathematical introduction to logic: An Algebraic Introduction to Mathematical Logic D.W. Barnes, J.M. Mack, 2013-06-29 This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a substantial course on abstract algebra. Consequently, our treatment of the subject is algebraic. Although we assume a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of the exercises. We also assume a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model of logic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based--rather, any conclusions to be drawn about the foundations of mathematics come only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory. |
| a mathematical introduction to logic: Elements of Set Theory Herbert B. Enderton, 1977-05-23 This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning. |
| a mathematical introduction to logic: A Mathematical Introduction to Logic Herbert Enderton, 2020-02-15 This title offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. |
| a mathematical introduction to logic: Mathematical Logic H.-D. Ebbinghaus, J. Flum, Wolfgang Thomas, 2013-03-14 This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming. |
| a mathematical introduction to logic: An Introduction to Mathematical Logic and Type Theory Peter B. Andrews, 2002-07-31 In case you are considering to adopt this book for courses with over 50 students, please contact ties.nijssen@springer.com for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. |
| a mathematical introduction to logic: Modern Mathematical Logic Joseph Mileti, 2022-09-22 This textbook gives a comprehensive and modern introduction to mathematical logic at the upper-undergraduate and beginning graduate level. |
| a mathematical introduction to logic: Introduction to Elementary Mathematical Logic Abram Aronovich Stolyar, 1984-01-01 This lucid, non-intimidating presentation by a Russian scholar explores propositional logic, propositional calculus, and predicate logic. Topics include computer science and systems analysis, linguistics, and problems in the foundations of mathematics. Accessible to high school students, it also constitutes a valuable review of fundamentals for professionals. 1970 edition. |
| a mathematical introduction to logic: A Profile of Mathematical Logic Howard DeLong, 2012-09-26 This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work. |
| a mathematical introduction to logic: Introduction To Mathematical Logic (Extended Edition) Michal Walicki, 2016-08-12 This is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book presupposes only elementary background and can be used also for self-study by more ambitious students.Starting with the basics of set theory, induction and computability, it covers propositional and first order logic — their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts.Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules — of a high, though often neglected, pedagogical value — aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers.An overview of the history of logic precedes the main text, while informal analogies precede introduction of most central concepts. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of logic.This revised edition contains also, besides many new exercises, a new chapter on semantic paradoxes. An equivalence of logical and graphical representations allows us to see vicious circularity as the odd cycles in the graphical representation and can be used as a simple tool for diagnosing paradoxes in natural discourse. |
| a mathematical introduction to logic: A Concise Introduction to Mathematical Logic Wolfgang Rautenberg, 2010-07-01 Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised. |
| a mathematical introduction to logic: Introduction to Mathematical Logic Alonzo Church, 1996 A classic account of mathematical logic from a pioneering giant in the field Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic. Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979. At his death in 1995, Church was still regarded as the greatest mathematical logician in the world. |
| a mathematical introduction to logic: Introduction to Mathematical Logic Alonzo Church, 1965 |
| a mathematical introduction to logic: Mathematical Logic Joseph R. Shoenfield, 2018-05-02 This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject. It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers. |
| a mathematical introduction to logic: Forcing For Mathematicians Nik Weaver, 2014-01-24 Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the standard axioms of set theory, forcing has been seen by the general mathematical community as a subject of great intrinsic interest but one that is technically so forbidding that it is only accessible to specialists. In the past decade, a series of remarkable solutions to long-standing problems in C*-algebra using set-theoretic methods, many achieved by the author and his collaborators, have generated new interest in this subject. This is the first book aimed at explaining forcing to general mathematicians. It simultaneously makes the subject broadly accessible by explaining it in a clear, simple manner, and surveys advanced applications of set theory to mainstream topics. |
| a mathematical introduction to logic: Introduction to Mathematical Logic Jerome Malitz, 2012-12-06 This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic. There are virtually no prere quisites, although a familiarity with notions encountered in a beginning course in abstract algebra such as groups, rings, and fields will be useful in providing some motivation for the topics in Part III. An attempt has been made to develop the beginning of each part slowly and then to gradually quicken the pace and the complexity of the material. Each part ends with a brief introduction to selected topics of current interest. The text is divided into three parts: one dealing with set theory, another with computable function theory, and the last with model theory. Part III relies heavily on the notation, concepts and results discussed in Part I and to some extent on Part II. Parts I and II are independent of each other, and each provides enough material for a one semester course. The exercises cover a wide range of difficulty with an emphasis on more routine problems in the earlier sections of each part in order to familiarize the reader with the new notions and methods. The more difficult exercises are accompanied by hints. In some cases significant theorems are devel oped step by step with hints in the problems. Such theorems are not used later in the sequence. |
| a mathematical introduction to logic: Introduction to Mathematical Philosophy Bertrand Russell, 1920 |
| a mathematical introduction to logic: Philosophical and Mathematical Logic Harrie de Swart, 2018-11-28 This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. The reader will not only be provided with an introduction to classical logic, but to philosophical (modal, epistemic, deontic, temporal) and intuitionistic logic as well. The first chapter is an easy to read non-technical Introduction to the topics in the book. The next chapters are consecutively about Propositional Logic, Sets (finite and infinite), Predicate Logic, Arithmetic and Gödel’s Incompleteness Theorems, Modal Logic, Philosophy of Language, Intuitionism and Intuitionistic Logic, Applications (Prolog; Relational Databases and SQL; Social Choice Theory, in particular Majority Judgment) and finally, Fallacies and Unfair Discussion Methods. Throughout the text, the author provides some impressions of the historical development of logic: Stoic and Aristotelian logic, logic in the Middle Ages and Frege's Begriffsschrift, together with the works of George Boole (1815-1864) and August De Morgan (1806-1871), the origin of modern logic. Since if ..., then ... can be considered to be the heart of logic, throughout this book much attention is paid to conditionals: material, strict and relevant implication, entailment, counterfactuals and conversational implicature are treated and many references for further reading are given. Each chapter is concluded with answers to the exercises. Philosophical and Mathematical Logic is a very recent book (2018), but with every aspect of a classic. What a wonderful book! Work written with all the necessary rigor, with immense depth, but without giving up clarity and good taste. Philosophy and mathematics go hand in hand with the most diverse themes of logic. An introductory text, but not only that. It goes much further. It's worth diving into the pages of this book, dear reader! Paulo Sérgio Argolo |
| a mathematical introduction to logic: A Beginner's Guide to Mathematical Logic Raymond M. Smullyan, 2014-03-19 Combining stories of great writers and philosophers with quotations and riddles, this original text for first courses in mathematical logic examines problems related to proofs, propositional logic and first-order logic, undecidability, and other topics. 2014 edition. |
| a mathematical introduction to logic: Mathematical Logic through Python Yannai A. Gonczarowski, Noam Nisan, 2022-07-31 Using a unique pedagogical approach, this text introduces mathematical logic by guiding students in implementing the underlying logical concepts and mathematical proofs via Python programming. This approach, tailored to the unique intuitions and strengths of the ever-growing population of programming-savvy students, brings mathematical logic into the comfort zone of these students and provides clarity that can only be achieved by a deep hands-on understanding and the satisfaction of having created working code. While the approach is unique, the text follows the same set of topics typically covered in a one-semester undergraduate course, including propositional logic and first-order predicate logic, culminating in a proof of Gödel's completeness theorem. A sneak peek to Gödel's incompleteness theorem is also provided. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. Familiarity with proofs and basic proficiency in Python is assumed. |
| a mathematical introduction to logic: Mathematical Logic Stephen Cole Kleene, 2013-04-22 Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more. |
| a mathematical introduction to logic: A Tour Through Mathematical Logic Robert S. Wolf, 2005-12-31 A Tour Through Mathematical Logic provides a tour through the main branches of the foundations of mathematics. It contains chapters covering elementary logic, basic set theory, recursion theory, Gödel's (and others') incompleteness theorems, model theory, independence results in set theory, nonstandard analysis, and constructive mathematics. In addition, this monograph discusses several topics not normally found in books of this type, such as fuzzy logic, nonmonotonic logic, and complexity theory. |
| a mathematical introduction to logic: A First Course in Mathematical Logic and Set Theory Michael L. O'Leary, 2015-09-14 A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis. |
| a mathematical introduction to logic: Foundations of Mathematical Logic Haskell Brooks Curry, 1977-01-01 Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition. |
| a mathematical introduction to logic: First Course in Mathematical Logic Patrick Suppes, Shirley Hill, 2012-04-30 Rigorous introduction is simple enough in presentation and context for wide range of students. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers; universal specification and laws of identity; more. |
| a mathematical introduction to logic: Mathematical Logic and Model Theory Alexander Prestel, Charles N. Delzell, 2011-08-21 Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differ quite significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study. |
| a mathematical introduction to logic: A Course in Mathematical Logic for Mathematicians Yu. I. Manin, 2009-10-13 1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery. |
| a mathematical introduction to logic: The Elements of Mathematical Logic Paul C. Rosenbloom, 1950 This book is intended for readers who, while mature mathematically, have no knowledge of mathematical logic. We attempt to introduce the reader to the most important approaches to the subject, and, wherever possible within the limitations of space which we have set for ourselves, to give at least a few nontrivial results illustrating each of the important methods for attacking logical problems--Preface. |
| a mathematical introduction to logic: Popular Lectures on Mathematical Logic Hao Wang, 2014-09-22 Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author. |
| a mathematical introduction to logic: Fundamentals of Mathematical Logic Peter G. Hinman, 2018-10-08 This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic. |
| a mathematical introduction to logic: Introduction to Discrete Mathematics via Logic and Proof Calvin Jongsma, 2019-11-08 This textbook introduces discrete mathematics by emphasizing the importance of reading and writing proofs. Because it begins by carefully establishing a familiarity with mathematical logic and proof, this approach suits not only a discrete mathematics course, but can also function as a transition to proof. Its unique, deductive perspective on mathematical logic provides students with the tools to more deeply understand mathematical methodology—an approach that the author has successfully classroom tested for decades. Chapters are helpfully organized so that, as they escalate in complexity, their underlying connections are easily identifiable. Mathematical logic and proofs are first introduced before moving onto more complex topics in discrete mathematics. Some of these topics include: Mathematical and structural induction Set theory Combinatorics Functions, relations, and ordered sets Boolean algebra and Boolean functions Graph theory Introduction to Discrete Mathematics via Logic and Proof will suit intermediate undergraduates majoring in mathematics, computer science, engineering, and related subjects with no formal prerequisites beyond a background in secondary mathematics. |
| a mathematical introduction to logic: Concise Introduction to Logic and Set Theory Iqbal H. Jebril, Hemen Dutta, Ilwoo Cho, 2021-09-30 This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding. The book is designed for readers from various disciplines where mathematical logic and set theory play a crucial role. The book will be of interested to students and instructors in engineering, mathematics, computer science, and technology. |
| a mathematical introduction to logic: The Foundations of Mathematics Kenneth Kunen, 2009 Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth. |
| a mathematical introduction to logic: Metamathematics of First-Order Arithmetic Petr Hájek, Pavel Pudlák, 2017-03-02 A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic. |
| a mathematical introduction to logic: An Introduction to Mathematical Reasoning Peter J. Eccles, 2013-06-26 This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas. |
| a mathematical introduction to logic: Introduction to Logic (Teacher Guide) Jason Lisle, 2018-12-10 The vital resource for grading all assignments from the Introduction To Logic course, which includes:Instructional insights enhanced with worksheets and additional practice sheetsSpecial chapter reviews at the beginning of each new chapter worksheet created to help students and teachers grasp the scope of each section.OVERVIEW: Welcome to the world of logic. This logic course will both challenge and inspire students to be able to defend their faith against atheists and skeptics alike. Because learning logical terms and principles is often like learning a foreign language, the course has been developed to help students of logic learn the practical understanding of logical arguments. To make the course content easier to grasp, the schedule provides worksheets and practice sheets to help students better recognize logical fallacies, as well as review weeks for the quizzes and the final. The practice sheets in the back of the book offer practical study for both the final exam and for actual arguments you might encounter online or in the media.FEATURES: The calendar provides daily sessions with clear objectives and worksheets, quizzes, and tests, all based on the readings from the course book. |
A Mathematical Introduction to Logic, 2nd Edition - Internet Archive
troductory mathematics course in logic at the junior-senior level. The objectives are to present the important concepts and theorems of logic and to explain their significance and their relationship to the reader’s other mathematical work. Asatext,thebookcanbeusedincoursesanywherefrom …
A Mathematical Introduction to Logic - bookshelf.jrpotter.com
A Mathematical Introduction to Logic. Herbert B. Enderton. Contents. R Reference 2. R.1 ¶ Construction Sequence . . . . . . . . . . . . . . . . . . . . . . 2. R.2 ¶ Expression . . . . . . . . . . . . . . . . . . …
Introduction to Mathematical Logic - University of California, San …
mathematical logic is a branch of mathematics that attempts to understand and justify all mathematical reasoning. With the Soundness and Completeness The-orems for first-order …
Introduction to Mathematical Logic - cuni.cz
This is a compact introduction to some of the principal topics of mathematical logic. [n the belief that beginners should be exposed to the easiest and most natural proofs, I have used free …
Introduction to Mathematical Logic - LU
1. Introduction. What Is Logic, Really? Attention! In this book, predicate language is used as a synonym of first order language, formal theory – as a synonym of formal system, deductive …
B1.1 Logic - University of Oxford
Introduction 1. What is mathematical logic about? • provide a uniform, unambiguous language for mathematics • make precise what a proof is • explain and guarantee exactness, rigor and …
Introduction to Mathematical Logic - dspace.lu.lv
1. Introduction. What Is Logic, Really? WARNING! In this book, predicate language is used as a synonym of first order language, formal theory – as a synonym of formal system, deductive …
Introduction to Mathematical Logic - TU Dresden
We then introduce first-order logic, in several steps: we first introduce (first- order) structures. These are the objects that first-order logic is talking about.
INTRODUCTION TO MATHEMATICAL LOGIC - univie.ac.at
INTRODUCTION TO MATHEMATICAL LOGIC. VERA FISCHER. March 12, 2020: For current information of the covered mate-rial, please see Moodle and u:space websites of the lecture …
LECTURE NOTES: INTRODUCTION TO MATHEMATICAL …
Overview. In the first chapter, we study structures, formulas and introduce the Hilbert calculus. In the second chapter, we give an introduction to set theory. We begin informally with ordinals …
Introduction: What IS Mathematical Logic? - Johns Hopkins …
Thus, logic becomes a branch of mathematics. But not just that. Other branches of mathematics (graph theory, group theory, geometry, arithmetic, set theory) are formalizable in (elementary) …
Mathematical Logic Lecture 1: Introduction and background - IIT …
Mathematization/Formalization of the intuition is mathematical logic. Two streams of studying logic. use of logic : logic as a tool to study something else. properties of logic: since logic is …
A Mathematical Introduction to Logic - GBV
Contents. 1.0 Informal Remarks on Formal Languages. 1.1 The Language of Sentential Logic. 1.2 Truth Assignments. 1.3 A Parsing Algorithm. 1.4 Induction and Recursion. 1.5 Sentential …
A Mathematical Introduction to Logic - On-Line
CHAPTER ONE Sentential Logic 11 1.0 Informal Remarks on Formal Languages 11 1.1 The Language of Sentential Logic 13 1.2 Truth Assignments 20 1.3 A Parsing Algorithm 29 1.4 …
Logic: A Study Guide - Logic Matters
1. Peter Smith, Introduction to Formal Logic** (2nd edition, CUP, 2020; corrected version now freely downloadable from logicmatters.net/i ). The rst edition was the rst year text in …
Mathematical Logic 2016 - IIT Bombay
Topic 1.1. What is logic? Have you ever said to someone \be logical"? whatever your intuition was that is logic. Mathematization/Formalization of the intuition is mathematical logic. Two streams …
Beginning Mathematical Logic: A Study Guide - Logic Matters
how do you choose what to read? Beginning Mathematical Logic provides the necessary guide. It introduces the core topics and recommends the best books for studying these topics enjoyably …
LECTURE NOTES IN LOGIC - UCLA Mathematics
Our main aim in this flst chapter is to introduce the basic notions of logic and to prove G˜odel’s Completeness Theorem 1I.1, which is the flrst, fun- damental result of the subject.
Mathematical Logic - LMU
1 Introduction What is mathematical logic? Let us consider a simple theorem in group theory: A group is a triple (G; ;e) with Gis a set, G6=? : G G!G e2G such that the following axioms are …
ELEMENTARY MATHEMATICAL LOGIC: INTRODUCTION AND …
Introduction: What is Logic? Logic is traditionally defined as the study of reasoning. Mathematical Logic is, in particular, the study of reasoning as used in mathematics. Math-ematical reasoning …
An Invitation to Mathematical Logic - University of Illinois Chicago
logic at the University of Illinois Chicago. The heroes of most introductory logic texts are Godel and Turing.1 Cer-tainly the Godel’s Completeness and Incompleteness Theorems and …
A FIRST COURSE IN AND SET THEORY - MyMathsCloud
CONTENTS Preface xiii Acknowledgments xv List of Symbols xvii 1 Propositional Logic 1 1.1 Symbolic Logic 1 Propositions 2 Propositional Forms 5 Interpreting Propositional Forms 7
Chapter I: Introduction to Mathematical Fuzzy Logic
Chapter I: Introduction to Mathematical Fuzzy Logic 3 Truth-functionality is one of the design choices employed in (mainstream) mathe-matical fuzzy logic. In other words, mathematical …
Introduction to Mathematical Logic - Universitetet i Bergen
Introduction to Mathematical Logic (Extended Edition) errata 1. p.91. Exercise 2.10, in the second line, \... implies f(X) F(Y)." should be: \... implies f(X) f(Y)."
Notes on Mathematical Logic David W. Kueker - UMD
Introduction: What Is Logic? Mathematical logic is the study of mathematical reasoning. We do this by developing an abstract model of the process of reasoning in mathematics. We then …
Introduction to Mathematical Thinking - Colorado State …
Introduction to Mathematical Thinking Renzo Cavalieri NotesforStudentsof Math 235 FortCollins,Spring2020 Department of Mathematics, Colorado State University, Fort Collins, …
Introduction to Logic Introduction - Stanford University
Uses of Logic "Whether I am on a soccer field or at a robotics competition, I face a lot of situations where logic is necessary to make decisions." "I have always loved puzzles and like …
Mathematical Logic 2016 - IIT Bombay
Mathematical Logic 2016 Lecture 1: Introduction and background Instructor: Ashutosh Gupta TIFR, India Compile date: 2016-08-06. ... Mathematical Logic 2016 Instructor: Ashutosh Gupta …
A FIRST COURSE IN LOGIC - Heriot-Watt University
Aims. This is an introduction to rst order logic suitable for rst or second year mathematicians and computer scientists. There are three components to this course: propositional logic, Boolean …
Propositional Logic - Stanford University
Propositional Logic Propositional logic is a mathematical system for reasoning about propositions and how they relate to one another. Every statement in propositional logic consists of …
DanielW.Cunningham MathematicalLogic - De Gruyter
AlsoofInterest AdvancedMathematics AnInvitationinPreparationforGraduateSchool PatrickGuidotti,2022 ISBN978-3-11-078085-7,e-ISBN(PDF)978-3-11-078092-5
Mathematics TEXTBOOKS in MATHEMATICS TEXTBOOKS in …
an introduction to partial differential equations with matlab®, second edition mathew coleman introduction to the calculus of variations and control with modern applications john t. burns …
Mathematical Logic
Mathematical Logic Introduction on Modal Logics Chiara Ghidini FBK-irst, Trento, Italy 28 November 2013 Chiara Ghidini Mathematical Logic. TestBooks and Readings Hughes, G. E., …
Logic in Computer Science 1 Introduction - Department of …
Logic and Proof Hilary 2024 Logic in Computer Science James Worrell 1 Introduction When I was a student, even the topologists regarded mathematical logicians as living in outer space. …
INTRODUCTION TO FIRST ORDER LOGIC AND MODEL THEORY
1. Introduction: First Order Language A serious inquiry of mathematical logic appears challenging even at the begin-ning. Logic drives inferences from one mathematical statement to another; …
Introduction - Harvard University
141A MATHEMATICAL LOGIC I ASSAF SHANI 1. Introduction Before getting formal, let us recall some examples of mathematical structures. 1.1. Some mathematical structures. Here are …
Introduction to Logic - IIT Kanpur
Patrick Hurley, Concise introduction to Logic, Thomson / Wadsworth, 2007[standard Course book] Mendelson, Introduction to Mathematical Logic, pp:1-90 [Extra reading] Shawn Hedman, A …
A Concise Introduction To Mathematical Logic [PDF] - Piedmont …
Introduction To Mathematical Logic, a captivating work of fictional splendor that pulses with fresh feelings, lies an memorable trip waiting to be embarked upon. Written by a virtuoso wordsmith, …
Introduction to Logic: Problems and solutions - NPTEL
3 Syllogistic Logic 20 3.1 Lecture 11: Introduction and motivation for Syllogistic Logic . . . . . . . . . 20 3.1.1 Name the form of each of the following categorical statements ( A , E, I , or O ). …
Mathematical Logic - UniTrento
Mathematical Logic Introduction on Modal Logics Chiara Ghidini FBK-irst, Trento, Italy 28 November 2013 Chiara Ghidini Mathematical Logic. TestBooks and Readings Hughes, G. E., …
Mathematical Logic
Mathematical Logic Natural Deduction and Hilbert style Propositional reasoning. Introduction to decision procedures Chiara Ghidini FBK-IRST, Trento, Italy ... there is an introduction rule ( I) …
Symbolic Logic - Tony Roy
mathematical logic with metalogical components often cast only the barest glance at mathematical induction or even the very idea of reasoning from definitions, a first ... ematical Logic, and …
A Mathematical Introduction to Logic - GBV
A Mathematical Introduction to Logic.••-•• Second Edition Herbert B. Enderton A,. . l'ni\iirsit\ ui ... CHAPTER TWO First-Order Logic 67 2.0 Preliminary Remarks 67 2.1 First-Order Languages …
A Mathematical Introduction to Modal Logic - nesinkoyleri.org
For philosophers, modal logic is a powerful tool for se-mantics. Many concepts in philosophy of language can be formalized in modal logic. Computer scientists, on the other hand, use modal …
A Mathematical Introduction to Modal Logic - Can Baskent
For philosophers, modal logic is a powerful tool for se-mantics. Many concepts in philosophy of language can be formalized in modal logic. Computer scientists, on the other hand, use modal …
Gerard O’Regan Guide to Discrete Mathematics
gistic logic, stoic logic, fallacies, and paradoxes. Boole’s symbolic logic and its application to digital computing, and Frege’s work on predicate logic are discussed. Chapter 15 provides an …
Fundamentals of Mathematical Logic - Springer
9. Formulate the laws of algebra of logic. 10. Specify the main types of proof of the truth of propositions. 11. Formulate a mathematical induction principle. 1.2 ProblemsforChapter …
A Mathematical Introduction to Logic - On-Line
Contents PREFACE ix INTRODUCTION xi CHAPTER ZERO Useful Facts about Sets 1 CHAPTER ONE Sentential Logic 11 1.0 Informal Remarks on Formal Languages 11 1.1 The …
MAT 309: Introduction to Mathematical Logic, Winter 2018
Textbook \A Friendly Introduction to Mathematical Logic" (2nd Edition) by Christopher C. Leary and Lars Kristiansen Available online and at the UofT bookstore for $27.10. Course …
MATH 250 | Introduction to Mathematical Logic. - College of …
MATH 250 | Introduction to Mathematical Logic. Most intermediate and advanced mathematics courses involve proving theorems. Mathematical logic is a formal analysis of proofs. If starts by …
STUDENT MATHEMATICAL LIBRARY Volume 88 Hilbert’s Tenth …
[Ho] R.Hodel,An Introduction to Mathematical Logic,DoverPublications,New York, 2013. [Hod] A.Hodges,Alan Turing: the enigma,Thecentenaryedition,PrincetonUni-versity Press, Princeton, …
Set Theory: A First Course - Cambridge University Press
specializing in set theory and mathematical logic. He is a member of the Association for Symbolic Logic, the American Mathematical Society, and the Mathematical Association of America. …
PHIL 12A - Introduction to Logic - University of California, Berkeley
PHIL 12A - Introduction to Logic Prof. Wes Holliday UC Berkeley Author: PHIL 12A - Introduction to Logic Subject: Resumé of PHIL 12A - Introduction to Logic Keywords: PHIL 12A - …
K. Tanaka Introduction Logic and Computation I
Logic and Computation K. Tanaka Introduction §1.1 Automata and Monoids Regular language Formal definition of NFA Regular language and NFA From NFA to DFA Summary Appendix …
The Project Gutenberg eBook #41654: An Introduction to Mathematical …
17 Feb 2013 · mathematical logic is relevant to philosophy. For this reason, as well as on account of the intrinsic importance of the sub-ject, some purpose may be served by a succinct account …
First-Order Logic - Stanford University
What is First-Order Logic? First-order logic is a logical system for reasoning about properties of objects. Augments the logical connectives from propositional logic with predicates that …
Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems
Introduction to fuzzy sets, fuzzy logic, and fuzzy control systems / Guanrong Chen, Trung Tat Pham. p. cm. Includes bibliographical references and index. ISBN 0-8493-1658-8 (alk. paper) …
Appendix to the Study Guide - Logic Matters
Hodel, An Introduction to Mathematical Logic, 199523 12. Goldstern & Judah, The Incompleteness Phenomenon: A New Course in Mathematical Logic, 199526 13. Rautenberg, …
Lecture 7: Set Theory and Logic - Harvard University
Lecture 7: Set Theory and Logic 7.1. S ets are fundamental building blocks of mathematics. While logic gives a language and rules for doing mathematics, set theory provides the material for …
A Concise Introduction to Mathematical Logic - fu-berlin.de
A Concise Introduction to Mathematical Logic Author: Wolfgang Rautenberg, Berlin Subject: Traditional logic as a part of philosophy is one of the oldest scientific disciplines. Mathematical …
Introduction to Logic, PHILOS W12A Summer 2020
Symbolic logic is by nature a mathematical subject, but the course does not presuppose any prior coursework in mathematics—only an openness to mathematical reasoning. The online …
Third Edition A Concise Introduction to Mathematical Logic
A Concise Introduction to Mathematical Logic Wolfgang Rautenberg A Concise Introduction to Mathematical Logic Third Edition Traditional logic as a part of philosophy is one of the oldest …
A Mathematical Introduction to Logic, 2nd Edition
Introduction S ymbolic logic is a mathematical model of deductive thought. Or at least that was true originally; as with other branches of mathematics it has grown beyond the circumstances …
Set Theory and Foundations of Mathematics: An Introduction to ...
Introduction Set theory and mathematical logic compose the foundation of pure mathematics. Using the axioms of set theory, we can con-struct our universe of discourse, beginning with …
Introduction To Mathematical Structures And Proof Full PDF
Introduction to Mathematical Proof - University of Scranton Learn the basics of mathematical proof, including formal proof systems, logic, quantifiers, and induction. This web page …
Introduction to Mathematical Proof - University of Scranton
Introduction to Mathematical Proof Lecture Notes 1 What is a proof? Simply stated A proof is an explanation of why a statement is objectively correct. Thus, we have two goals for our proofs. • …
Discrete Mathematics: An Open Introduction
Logic and Set Theory Logic is the study of consequence. Given a few mathematical statements or facts, we would like to be able to draw some conclusions. For example, if I told you that a …
Introduction to mathematical arguments - University of …
Introduction to mathematical arguments (background handout for courses requiring proofs) by Michael Hutchings A mathematical proof is an argument which convinces other people that …
An Introduction to Mathematical Logic - pgadey.ca
2.Enderton, An Introduction to Mathematical Logic 3.Marker, Model Theory: An Introduction 4.Hodges, A Shorter Model Theory 5.Chang & Keisler, Model Theory 6.Marker, Model Theory …
Mathematical Logic and Computation - Cambridge University …
This new book on mathematical logic by Jeremy Avigad gives a t horough introduc-tion to the fundamental results and methods of the subject fr om the syntactic point of view, emphasizing …
