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Research papers

Stable theories of Frechet-powers

E. A. Palyutin

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

Abstract: Elementary theories of Frechet-powers $A^F$ of structures $A$ are investigated. We put a special emphasis on the study of such theories under the condition of stability as well as on constructions of their models containing a given sets $X$ which are minimal in the sense that, the dimensions of independent sets represented in $X$ do not increase. The basis results of the paper are the characterization of forking (Theorem 2) and a theorem on preservation of dimension in $\lambda$-positive envelopes (Theorem 3).

Keywords: model theory, elementary theories, stability.

UDC: 510.67

MSC: 03C45

Received December 23, 2008, published December 28, 2008

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