Translations of Mathematical Monographs 1993; 122 pp; hardcover Volume: 117 ISBN10: 0821845861 ISBN13: 9780821845868 List Price: US$59 Member Price: US$47.20 Order Code: MMONO/117
 The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a oneplace function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories, this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions. Readership Research mathematicians. Table of Contents  Survey of preliminary results and terminology
 Three types of uncountably categorical structures
 Classification of infinite locally finite homogeneous pregeometries
 Description of strongly minimal quasialgebras
 Global structure of uncountably categorical structures
