Memoirs of the American Mathematical Society 2014; 80 pp; softcover Volume: 230 ISBN10: 0821894757 ISBN13: 9780821894750 List Price: US$65 Individual Members: US$39 Institutional Members: US$52 Order Code: MEMO/230/1081
 Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of firstorder theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations. Table of Contents  History and motivation
 Introduction
 Borel sets, \(\Delta_1^1\) sets and infinitary logic
 Generalizations from classical descriptive set theory
 Complexity of isomorphism relations
 Reductions
 Open questions
 Bibliography
