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June 2006 On PAC and bounded substructures of a stable structure
Anand Pillay, Dominika Polkowska
J. Symbolic Logic 71(2): 460-472 (June 2006). DOI: 10.2178/jsl/1146620152

Abstract

We introduce and study the notions of a PAC-substructure of a stable structure, and a bounded substructure of an arbitrary substructure, generalizing [10]. We give precise definitions and equivalences, saying what it means for properties such as PAC to be first order, study some examples (such as differentially closed fields) in detail, relate the material to generic automorphisms, and generalize a “descent theorem” for pseudo-algebraically closed fields to the stable context. We also point out that the elementary invariants of pseudo-algebraically closed fields from [6] are also valid for pseudo-differentially closed fields.

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Anand Pillay. Dominika Polkowska. "On PAC and bounded substructures of a stable structure." J. Symbolic Logic 71 (2) 460 - 472, June 2006. https://doi.org/10.2178/jsl/1146620152

Information

Published: June 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1100.03027
MathSciNet: MR2225887
Digital Object Identifier: 10.2178/jsl/1146620152

Rights: Copyright © 2006 Association for Symbolic Logic

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Vol.71 • No. 2 • June 2006
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