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JSYML
2007

Stable definability and generic relations

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Stable definability and generic relations
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.
Byunghan Kim, Rahim Moosa
Added 16 Dec 2010
Updated 16 Dec 2010
Type Journal
Year 2007
Where JSYML
Authors Byunghan Kim, Rahim Moosa
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