### Model Companions of for Stable T

John T. Baldwin and Saharon Shelah
Source: Notre Dame J. Formal Logic Volume 42, Number 3 (2001), 129-142.

#### 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 (nfcp). For any theory T, form a new theory 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 has a model companion. The proof involves some interesting new consequences of the nfcp.

First Page:
Primary Subjects: 03C45
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1063372196
Digital Object Identifier: doi:10.1305/ndjfl/1063372196
Mathematical Reviews number (MathSciNet): MR2010177
Zentralblatt MATH identifier: 1034.03040

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