This book presents both axiomatic and descriptive set theory, targeting upper-level undergraduate and beginning graduate students. It aims to equip them for advanced studies in set theory, mathematical logic, and other mathematical fields, including analysis, topology, and algebra.

The book is designed as a flexible and accessible text for a one-semester introductory in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered through the text.

This new edition includes additional topics on trees, ordinal functions, and sets, along with numerous new exercises. The presentation has been improved, and several typographical errors have been corrected.

Contents:

• Introduction


• Review of Sets and Logic


• Zermelo–Fraenkel Set Theory


• Natural Numbers and Countable Sets


• Ordinal Numbers and the Transfinite


• Cardinality and the Axiom of Choice


• Real Numbers


• Models of Set Theory


• Ramsey Theory

Readership: Upper level undergraduate or beginning graduate students interested in set theory and mathematical logic.

Review of the First Edition:'The book was developed over many years from class notes for a set theory course at the University of Florida, which has been taught to advanced undergraduates as well as beginning graduate students. It gives a solid introduction to axiomatic set theory and presents several interesting applications.' - MathSciNet