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 universal...

This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology. These include effective versions of Borel equivalence, Borel reducibility and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSF-supported annual Southeastern Logic Symposium.

This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specia...