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December 2007 Stable definability and generic relations
Byunghan Kim, Rahim Moosa
J. Symbolic Logic 72(4): 1163-1176 (December 2007). DOI: 10.2178/jsl/1203350778

Abstract

An amalgamation base p in a simple theory is stably definable if its canonical base is interdefinable with the set of canonical parameters for the φ-definitions of p as φ ranges through all stable formulae. A necessary condition for stably definability is given and used to produce an example of a supersimple theory with stable forking having types that are not stably definable. This answers negatively a question posed in [8]. A criterion for and example of a stably definable amalgamation base whose restriction to the canonical base is not axiomatised by stable formulae are also given. The examples involve generic relations over non CM-trivial stable theories.

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Byunghan Kim. Rahim Moosa. "Stable definability and generic relations." J. Symbolic Logic 72 (4) 1163 - 1176, December 2007. https://doi.org/10.2178/jsl/1203350778

Information

Published: December 2007
First available in Project Euclid: 18 February 2008

zbMATH: 1130.03025
MathSciNet: MR2371197
Digital Object Identifier: 10.2178/jsl/1203350778

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 4 • December 2007
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