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Countably Categorical Structures with n‐Degenerate Algebraic Closure
Author(s) -
Vassiliev Evgueni V.
Publication year - 1999
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19990450108
Subject(s) - categorical variable , mathematics , degenerate energy levels , algebraic number , algebraic closure , closure (psychology) , pure mathematics , lattice (music) , class (philosophy) , discrete mathematics , mathematical analysis , computer science , artificial intelligence , differential algebraic equation , ordinary differential equation , statistics , physics , quantum mechanics , economics , acoustics , market economy , differential equation
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.