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

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