Modern Mathematical Logic

This textbook gives a comprehensive and modern introduction to mathematical logic at the upper-undergraduate and beginning graduate level.

Joseph Mileti (Author)

9781108833141, Cambridge University Press

Hardback, published 22 September 2022

550 pages
25.4 x 17.8 x 2.9 cm, 1.1 kg

Mileti has written a careful, rigorous treatment of a broad range of topics in mathematical logic. This is a valuable addition to the literature. Daniel J. Velleman, Amherst College

This textbook gives a complete and modern introduction to mathematical logic. The author uses contemporary notation, conventions, and perspectives throughout, and emphasizes interactions with the rest of mathematics. In addition to covering the basic concepts of mathematical logic and the fundamental material on completeness, compactness, and incompleteness, it devotes significant space to thorough introductions to the pillars of the modern subject: model theory, set theory, and computability. Requiring only a modest background of undergraduate mathematics, the text can be readily adapted for a variety of one- or two-semester courses at the upper-undergraduate or beginning-graduate level. Numerous examples reinforce the key ideas and illustrate their applications, and a wealth of classroom-tested exercises serve to consolidate readers' understanding. Comprehensive and engaging, this book offers a fresh approach to this enduringly fascinating and important subject.

Preface
Acknowledgements
1. Introduction
2. Induction and recursion
3. Propositional logic
4. First-order logic: languages and structures
5. Relationships between structures
6. Implication and compactness
7. Model theory
8. Axiomatic set theory
9. Ordinals, cardinals, and choice
10. Set-theoretic methods in model theory
11. Computable sets and functions
12. Logic, computation, and incompleteness
Appendix: mathematical background
References
Index.

Subject Areas: Mathematical logic [PBCD], Philosophy: logic [HPL]