A Friendly Introduction to Mathematical Logic

At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary’s user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory.

The text is designed to be used either in an upper division undergraduate classroom, or for self study.

Updating the 1st Edition’s treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel’s First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.

Table of Contents

1 Structures and Languages

2 Deductions

3 Completeness and Compactness

4 Incompleteness from Two Points of View

5 Syntactic Incompleteness Groundwork

6 The Incompleteness Theorems

7 Computability Theory

8 Summing Up, Looking Ahead

Appendix: Just Enough Set Theory to Be Dangerous