Journal of Symbolic Logic

Stable definability and generic relations

Byunghan Kim and Rahim Moosa

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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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J. Symbolic Logic, Volume 72, Issue 4 (2007), 1163-1176.

First available in Project Euclid: 18 February 2008

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Kim, Byunghan; Moosa, Rahim. Stable definability and generic relations. J. Symbolic Logic 72 (2007), no. 4, 1163--1176. doi:10.2178/jsl/1203350778.

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