About the Book: Notes on Set Theory The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. At the same time, it is often viewed as a foundation of mathematics so that in the most prevalent, current mathematical practice to make a notion precise simply means to define it in set theory. This book tries to do justice to both aspects of the subject: it gives a solid introduction to pure set theory through transfinite recursion and the construction of the cumulative hierarchy of sets (including the basic results that have applications to computer science), but it also attempts to explain precisely how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author added solutions to the exercises, and rearranged and reworked the text in several places to improve the presentation. The book is aimed at advanced undergraduate or beginning graduate mathematics students and at mathematically minded graduate students of computer science and philosophy. Contents Chapter 1. Introduction Chapter 2. Equinumerosity Chapter 3. Paradoxes and axioms Chapter 4. Are sets all there is? Chapter 5. The natural numbers Chapter 6. Fixed points Chapter 7. Well ordered sets Chapter 9. Choice's consequences Chapter 10. Baire space Chapter 11. Replacement and other axioms Chapter 12. Ordinal numbers Appendix A. The real numbers Appendix B. Axioms and universes Solutions to the exercises in Chapters Index