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Uncountably Categorical Theories (Translations of Mathematical Monographs)
Rok: 1993
ISBN: 9780821845868
OKCZID: 110760776
Citace (dle ČSN ISO 690):
ZILBER, Boris. Uncountably categorical theories. Providence, R.I.: American Mathematical Society, c1993. vi, 122 s. Translations of mathematical monographs, v. 117.
Anotace
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 one-place 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.