Open Access
2001 Model Companions of $T_{\rm Aut}$ for Stable T
John T. Baldwin, Saharon Shelah
Notre Dame J. Formal Logic 42(3): 129-142 (2001). DOI: 10.1305/ndjfl/1063372196


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 (nfcp). 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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John T. Baldwin. Saharon Shelah. "Model Companions of $T_{\rm Aut}$ for Stable T." Notre Dame J. Formal Logic 42 (3) 129 - 142, 2001.


Published: 2001
First available in Project Euclid: 12 September 2003

zbMATH: 1034.03040
MathSciNet: MR2010177
Digital Object Identifier: 10.1305/ndjfl/1063372196

Primary: 03C45

Keywords: expansion by automorphism , stability

Rights: Copyright © 2001 University of Notre Dame

Vol.42 • No. 3 • 2001
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