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On PAC and bounded substructures of a stable structure

Published online by Cambridge University Press:  12 March 2014

Anand Pillay  and
Dominika Polkowska
Anand Pillay
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK. E-mail: pillay@maths.leeds.ac.uk
Dominika Polkowska
Affiliation:
St. Cecilia Novitiate, 801 Dominion Drive, Nashville, TN 37228, USA
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 2 , June 2006 , pp. 460 - 472
Copyright
Copyright © Association for Symbolic Logic 2006

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