Introduction to Mathematical Logic 6th Edition by Elliott Mendelson, ISBN-13: 978-1482237726

Introduction to Mathematical Logic 6th Edition by Elliott Mendelson, ISBN-13: 978-1482237726

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Publisher: ‎ Routledge; 6th edition (July 24, 2015)
Language: ‎ English
514 pages
ISBN-10: ‎ 1482237725
ISBN-13: ‎ 978-1482237726

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.

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: GÃ¶del Numbers

The Fixed-Point Theorem: GÃ¶delâ€™s Incompleteness Theorem

Recursive Undecidability: Churchâ€™s Theorem

Nonstandard Models

Axiomatic Set Theory

An Axiom System

Ordinal Numbers

Equinumerosity: Finite and Denumerable Sets

Hartogsâ€™ Theorem: Initial Ordinalsâ€”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 Kleeneâ€“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

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.

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