✦ LIBER ✦

Countably Categorical Structures with n-Degenerate Algebraic Closure

✍ Scribed by Evgueni V. Vassiliev

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 583 KB
Volume: 45
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19990450108

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✦ Synopsis

Abstract

We study the class of ω‐categorical structures with n‐degenerate algebraic closure for some n ε ω, which includes ω‐categorical structures with distributive lattice of algebraically closed subsets (see [4]), and in particular those with degenerate (trivial) algebraic closure. We focus on the models of ω‐categorical universal theories, absolutely ubiquitous structures, and ω‐categorical structures generated by an indiscernible set. The assumption of n‐degeneracy implies total categoricity for the first class, stability for the second, and ω‐stability for the third.

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