This article is cited in 1 paper

Elementary Pairs of Primitive Normal Theories

E. A. Palyutin

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

Abstract: The main objective of the paper is proving that classes of primitive normal, primitive bound, antiadditive, and additive theories are closed under $P$-expansions. This phenomenon is quite remarkable, for the main “structure” classes of theories studied within model theory (such as stable, totally transcendental, etc.) do not possess such a property. Furthermore, it is proved that primitive bound theories are $P$-stable, and we furnish an example of a primitive bound theory with models that are not primitive bound.

Keywords: elementary pairs, primitive normal theory, primitive bound theory, antiadditive theory, additive theory, primitive bound model.

UDC: 510.67:512.57

Received: 19.12.2002

 English version: Algebra and Logic, 2004, 43:3, 179–189

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