A Mathematical Introduction to Logic
Herbert B. Enderton
Second Edition
Table of Contents
Preface
Introduction
Chapter Zero --- Useful Facts About Sets
Chapter One --- Sentential Logic
1.0 Informal Remarks on Formal Languages
1.1 The Language of Sentential Logic
1.2 Truth Assignments
1.3 A Parsing Algorithm
1.4 Induction and Recursion
1.5 Sentential Connectives
1.6 Switching Circuits
1.7 Compactness and Effectiveness
Chapter Two --- First-order Logic
2.0 Preliminary Remarks
2.1 First-Order Languages
2.2 Truth and Models
2.3 A Parsing Algorithm
2.4 A Deductive Calculus
2.5 Soundness and Completeness Theorems
2.6 Models of Theories
2.7 Interpretations between Theories
2.8 Nonstandard Analysis
Chapter Three --- Undecidability
3.0 Number Theory
3.1 Natural Numbers with Successor
3.2 Other Reducts of Number Theory
3.3 A Subtheory of Number Theory
3.4 Arithmetization of Syntax
3.5 Incompleteness and Undecidability
3.6 Recursive Functions
3.7 Second Incompleteness Theorem
3.8 Representing Exponentiation
Chapter Four --- Second-order Logic
4.1 Second-Order Languages
4.2 Skolem Functions
4.3 Many-Sorted Logic
4.4 General Structures
Suggestions for Further Reading
List of Symbols
Index