Introduction to Mathematical Logic, Fifth Edition / Edition 5

Introduction to Mathematical Logic, Fifth Edition / Edition 5

by Elliott Mendelson
Pub. Date:
Taylor & Francis

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Introduction to Mathematical Logic, Fifth Edition / Edition 5

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 Gödel, 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.

Product Details

ISBN-13: 9781584888765
Publisher: Taylor & Francis
Publication date: 08/07/2009
Series: Discrete Mathematics and Its Applications Series
Edition description: New Edition
Pages: 494
Product dimensions: 6.20(w) x 9.40(h) x 1.30(d)

Table of Contents

The Propositional Calculus

Propositional Connectives. Truth Tables


Adequate Sets of Connectives

An Axiom System for the Propositional Calculus

Independence. Many-Valued Logics

Other Axiomatizations

First-Order Logic and Model Theory


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


Algorithms. Turing Machines


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




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