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Stable definability and generic relations

Published online by Cambridge University Press:  12 March 2014

Byunghan Kim  and
Rahim Moosa
Byunghan Kim
Affiliation:
Yonsei University, Department of Mathematics, 134 Shinchon-Dong, Seodaemun-Gu Seoul 120-749, Korea. E-mail: [email protected]
Rahim Moosa
Affiliation:
University of Waterloo, Department of Pure Mathematics 200 University Avenue West Waterloo, Ontario N2L 3G1, Canada. E-mail: [email protected]
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Abstract

An amalgamation base p in a simple theory is stably definable if its canonical base is interde-finable 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
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 4 , December 2007 , pp. 1163 - 1176
Copyright
Copyright © Association for Symbolic Logic 2007

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References

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