Notes on Set Theory

The axiomatic theory of sets is a vibrant part of pure mathematics, and is also viewed as a foundation of mathematics. This book addresses both pure math and the fundamentals. The new edition is reworked and expanded for improved presentation.

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: it gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and rearranged and reworked the text to improve the presentation. The book is geared to advanced undergraduate or beginning graduate mathematics students and mathematically minded graduate students in computer science and philosophy.

Author is an excellent writer and expositor Treats unusual topics, such as the the continuous least fixed-point theorem and the Baire space Includes solutions to selected exercises, but not to the more challenging problems Includes supplementary material: sn.pub/extras

Inhalt
Equinumerosity.- Paradoxes and Axioms.- Are Sets All There is?.- The Natural Numbers.- Fixed Points.- Well Ordered Sets.- Choices.- Choice's Consequences.- Baire Space.- Replacement and Other Axioms.- Ordinal Numbers.