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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
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/27588459
Page Count: 13
You can always find the topics here!Topics: Algebra, Cardinality, Automorphisms, First order theories, Model theory, Differentials, Axioms, Induced substructures, Polynomials, Isomorphism
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We introduce and study the notions of a PAC-substructure of a stable structure, and a bounded substructure of an arbitrary substructure, generalizing . 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  are also valid for pseudo-differentially closed fields.
The Journal of Symbolic Logic © 2006 Association for Symbolic Logic