Introduction to Mathematical Logic, Fifth Edition

Introduction to Mathematical Logic, Fifth Edition

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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 Godel, Church, Kleene, Rosser, and Turing. New to the Fifth Edition A new section covering basic ideas and results about nonstandard models of number theoryA second appendix that introduces modal propositional logicAn 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 more

Product details

  • Electronic book text | 494 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • Revised
  • 5th Revised edition
  • very heavy equations, 1000+; 28 Illustrations, black and white
  • 1584888776
  • 9781584888772

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 Ashbachershow more

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. Godel Numbers The Fixed-Point Theorem. Godel'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 Indexshow more

About Elliott Mendelson

Elliott Mendelson is professor emeritus in the Department of Mathematics at Queens more