## 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.

### MSC:

 03C45 Classification theory, stability, and related concepts in model theory
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### References:

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