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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DOI 10.1305/ndjfl/1063372196
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References found in this work BETA

Generic Structures and Simple Theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
The Strict Order Property and Generic Automorphisms.Hirotaka Kikyo & Saharon Shelah - 2002 - Journal of Symbolic Logic 67 (1):214-216.
Les Beaux Automorphismes.Daniel Lascar - 1991 - Archive for Mathematical Logic 31 (1):55-68.
Model Companions of Theories with an Automorphism.Hirotaka Kikyo - 2000 - Journal of Symbolic Logic 65 (3):1215-1222.
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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Citations of this work BETA

Model Theoretic Dynamics in Galois Fashion.Daniel Max Hoffmann - 2019 - Annals of Pure and Applied Logic 170 (7):755-804.
The Metamathematics of Random Graphs.John T. Baldwin - 2006 - Annals of Pure and Applied Logic 143 (1-3):20-28.
Grouplike Minimal Sets in ACFA and in T A.Alice Medvedev - 2010 - Journal of Symbolic Logic 75 (4):1462-1488.

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