Model Companions of $T_{\rm Aut}$ for Stable T

Notre Dame Journal of Formal Logic 42 (3):129-142 (2001)
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Abstract

We introduce the notion T does not omit obstructions. If a stable theory does not admit obstructions then it does not have the finite cover property . For any theory T, form a new theory $T_{\rm Aut}$ 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 $T_{\rm Aut}$ has a model companion. The proof involves some interesting new consequences of the nfcp

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2010-08-24

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References found in this work

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Model companions of theories with an automorphism.Hirotaka Kikyo - 2000 - Journal of Symbolic Logic 65 (3):1215-1222.
Les beaux automorphismes.Daniel Lascar - 1991 - Archive for Mathematical Logic 31 (1):55-68.
The definable multiplicity property and generic automorphisms.Hirotaka Kikyo & Anand Pillay - 2000 - Annals of Pure and Applied Logic 106 (1-3):263-273.

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