Set Theory, Logic and their Limitations
This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Goedel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.
- Paperback | 300 pages
- 153 x 228 x 15mm | 510g
- 23 May 1996
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge, United Kingdom
Table of contents
Mathematical induction; 1. Sets and classes; 2. Relations and functions; 3. Cardinals; 4. Ordinals; 5. The axiom of choice; 6. Finite cardinals and alephs; 7. Propositional logic; 8. First order logic; 9. Facts from recursion theory; 10. Limitative results; Appendix: Skolem's paradox.
' ... written by an excellent mathematician ... I very much like the way the author explains things.' European Mathematical Society "...a concise and polished text..." J.M. Plotkin, Mathematical Reviews