Model companions of \(T_{\operatorname{Aut}}\) for stable \(T\). (English) Zbl 1034.03040

Summary: We introduce the notion \(T\) does not admit obstructions. If a stable theory does not admit obstructions then it does not have the finite cover property (nfcp). For any theory \(T\), form a new theory \(T_{\text{Aut}}\) by adding a new unary function symbol and axioms asserting it is an automorphism. The main result of the paper asserts the following: If \(T\) is a stable theory, \(T\) does not admit obstructions if and only if \(T_{\text{Aut}}\) has a model companion. The proof involves some interesting new consequences of the nfcp.


03C45 Classification theory, stability, and related concepts in model theory
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