Stably Definable Classes of Theories

E. A. Palyutin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: A question is studied as to which properties (classes) of elementary theories can be defined via generalized stability. We present a topological account of such classes. It is stated that some well-known classes of theories, such as strongly minimal, $o$-minimal, simple, etc., are stably definable, whereas, for instance, countably categorical, almost strongly minimal, $\omega$-stable ones, are not.

Keywords: elementary theory, stably definable class.

UDC: 510.67: 512.57

Received: 29.12.2004

 English version: Algebra and Logic, 2005, 44:5, 326–335

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