A Mathematical Introduction to Logic

A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today’s undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

Table of Contents

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