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On PAC and Bounded Substructures of a Stable Structure

Anand Pillay and Dominika Polkowska
The Journal of Symbolic Logic
Vol. 71, No. 2 (Jun., 2006), pp. 460-472
Stable URL: http://www.jstor.org/stable/27588459
Page Count: 13
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On PAC and Bounded Substructures of a Stable Structure
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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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