Introduction to Mathematical Logic, Fifth Edition

Introduction to Mathematical Logic, Fifth Edition

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Description

Retaining all the key features of the previous editions, Introduction to Mathematical Logic, Fifth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Goedel, Church, Kleene, Rosser, and Turing.


New to the Fifth Edition








A new section covering basic ideas and results about nonstandard models of number theory
A second appendix that introduces modal propositional logic
An expanded bibliography
Additional exercises and selected answers








This long-established text continues to expose students to natural proofs and set-theoretic methods. Only requiring some experience in abstract mathematical thinking, it offers enough material for either a one- or two-semester course on mathematical logic.
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Product details

  • Hardback | 494 pages
  • 157.48 x 236.22 x 30.48mm | 861.82g
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • New edition
  • 5th New edition
  • very heavy equations, 1000+; 28 Illustrations, black and white
  • 1584888768
  • 9781584888765
  • 625,535

Table of contents

The Propositional Calculus


Propositional Connectives. Truth Tables


Tautologies


Adequate Sets of Connectives


An Axiom System for the Propositional Calculus


Independence. Many-Valued Logics


Other Axiomatizations


First-Order Logic and Model Theory


Quantifiers


First-Order Languages and Their Interpretations. Satisfiability and Truth. Models


First-Order Theories


Properties of First-Order Theories


Additional Metatheorems and Derived Rules


Rule C


Completeness Theorems


First-Order Theories with Equality


Definitions of New Function Letters and Individual Constants


Prenex Normal Forms


Isomorphism of Interpretations. Categoricity of Theories


Generalized First-Order Theories. Completeness and Decidability


Elementary Equivalence. Elementary Extensions


Ultrapowers: Nonstandard Analysis


Semantic Trees


Quantification Theory Allowing Empty Domains


Formal Number Theory


An Axiom System


Number-Theoretic Functions and Relations


Primitive Recursive and Recursive Functions


Arithmetization. Goedel Numbers


The Fixed-Point Theorem. Goedel's Incompleteness Theorem


Recursive Undecidability. Church's Theorem


Nonstandard Models


Axiomatic Set Theory


An Axiom System


Ordinal Numbers


Equinumerosity. Finite and Denumerable Sets


Hartogs' Theorem. Initial Ordinals. Ordinal Arithmetic


The Axiom of Choice. The Axiom of Regularity


Other Axiomatizations of Set Theory


Computability


Algorithms. Turing Machines


Diagrams


Partial Recursive Functions. Unsolvable Problems


The Kleene-Mostowski Hierarchy. Recursively Enumerable Sets


Other Notions of Computability


Decision Problems


Appendix A: Second-Order Logic


Appendix B: First Steps in Modal Propositional Logic


Answers to Selected Exercises


Bibliography


Notation


Index
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Review quote

Since it first appeared in 1964, Mendelson's book has been recognized as an excellent textbook in the field. It is one of the most frequently mentioned texts in references and recommended reading lists ... This book rightfully belongs in the small, elite set of superb books that every computer science graduate, graduate student, scientist, and teacher should be familiar with.

-Computing Reviews, May 2010


"For the reviews of the previous editions see Zbl 192.01901, Zbl 498.03001, Zbl 681.03001 and Zbl 915.03002. The following are the significant changes in this edition: A new section (3.7) on the order type of a countable nonstandard model of arithmetic; a second appendix, Appendix B, on basic modal logic, in particular on the normal modal logics K, T, S4, and S5 and the relevant Kripke semantics for each; an expanded bibliography and additions to both the exercises and to the Answers to Selected Exercises, including corrections to the previous version of the latter."
-J. M. Plotkin, Zentralblatt MATH 1173


"Since its first edition, this fine book has been a text of choice for a beginner's course on mathematical logic. ... There are many fine books on mathematical logic, but Mendelson's textbook remains a sure choice for a first course for its clear explanations and organization: definitions, examples and results fit together in a harmonic way, making the book a pleasure to read. The book is especially suitable for self-study, with a wealth of exercises to test the reader's understanding."
-MAA Reviews, December 2009


Praise for the Fourth Edition


"In my work as a math teacher, researcher, author, and journal editor, I often encounter problems with a logical component. When that need arises, my first choice of reference is always this book. It is the most concise and readable introductory text I have ever encountered and it is a rare occasion when I fail to find the background material needed to solve the problem. It is also an excellent source of problems and I have pulled the ideas for many test questions from it over the years."
-Charles Ashbacher
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About Elliott Mendelson

Elliott Mendelson is professor emeritus in the Department of Mathematics at Queens College.
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Rating details

45 ratings
3.93 out of 5 stars
5 24% (11)
4 49% (22)
3 22% (10)
2 4% (2)
1 0% (0)
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