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December 2004 Local homogeneity
Bektur Baizhanov, John T. Baldwin
J. Symbolic Logic 69(4): 1243-1260 (December 2004). DOI: 10.2178/jsl/1102022221

Abstract

We study the expansion of stable structures by adding predicates for arbitrary subsets. Generalizing work of Poizat-Bouscaren on the one hand and Baldwin-Benedikt-Casanovas-Ziegler on the other we provide a sufficient condition (Theorem 4.7) for such an expansion to be stable. This generalization weakens the original definitions in two ways: dealing with arbitrary subsets rather than just submodels and removing the ‘small' or ‘belles paires' hypothesis. We use this generalization to characterize in terms of pairs, the ‘triviality' of the geometry on a strongly minimal set (Theorem 2.5). Call a set A benign if any type over A in the expanded language is determined by its restriction to the base language. We characterize the notion of benign as a kind of local homogenity (Theorem 1.7). Answering a question of [8] we characterize the property that M has the finite cover property over A (Theorem 3.9).

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Bektur Baizhanov. John T. Baldwin. "Local homogeneity." J. Symbolic Logic 69 (4) 1243 - 1260, December 2004. https://doi.org/10.2178/jsl/1102022221

Information

Published: December 2004
First available in Project Euclid: 2 December 2004

zbMATH: 1071.03019
MathSciNet: MR2135665
Digital Object Identifier: 10.2178/jsl/1102022221

Rights: Copyright © 2004 Association for Symbolic Logic

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Vol.69 • No. 4 • December 2004
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