Stable Definability and Generic Relations

Journal of Symbolic Logic 72 (4):1163 - 1176 (2007)
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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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References found in this work

A new strongly minimal set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
Generic structures and simple theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
A note on CM-Triviality and the geometry of forking.Anand Pillay - 2000 - Journal of Symbolic Logic 65 (1):474-480.
A note on CM-triviality and the geometry of forking.Anand Pillay - 2000 - Journal of Symbolic Logic 65 (1):474-480.

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