Introduction to Mathematical Logic: 6th Edition (Hardback) book cover

Introduction to Mathematical Logic

6th Edition

By Elliott Mendelson

Chapman and Hall/CRC

513 pages | 28 B/W Illus.

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pub: 2015-06-08
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Description

The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth 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 Gödel, Church, Kleene, Rosser, and Turing.

The sixth edition incorporates recent work on Gödel’s second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in the new edition for historical considerations. The text also offers historical perspectives and many new exercises of varying difficulty, which motivate and lead students to an in-depth, practical understanding of the material.

Reviews

Praise for the Fifth Edition

"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

"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

Table of Contents

Preface

Introduction

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: Gödel Numbers

The Fixed-Point Theorem: Gödel’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

Appendix C: A Consistency Proof for Formal Number Theory

Answers to Selected Exercises

Bibliography

Notations

Index

About the Author

Elliott Mendelson is professor emeritus at Queens College in Flushing, New York, USA. Dr. Mendelson obtained his bachelor's degree at Columbia University and his master's and doctoral degrees at Cornell University, and was elected afterward to the Harvard Society of Fellows. In addition to his other writings, he is the author of another CRC Press book Introducing Game Theory and Its Applications.

About the Series

Discrete Mathematics and Its Applications

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT028000
MATHEMATICS / Set Theory