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.

• Type: Journal
• Year: 2007
• Where: JSYML
• Authors: Byunghan Kim, Rahim Moosa
• Keywords: Amalgamation Base, Canonical Base, JSYML 2007, Stable Formulae