Mathematical Logic Quarterly 45 (1):85-94 (1999)

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 , and in particular those with degenerate 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
Keywords Universal theory  Homogeneous J‐tree  ω‐Categorical structure  n‐Degenerate algebraic closure  Absolutely ubiquitous structure  Distributive lattice of algebraically closed subsets
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DOI 10.1002/malq.19990450108
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Absolutely Ubiquitous Structures and ℵ0-Stability.Gábor Sági - 2010 - Bulletin of the Section of Logic 39 (1/2):43-51.

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