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On the type-definability of the binding group in simple theories

Published online by Cambridge University Press:  12 March 2014

Bradd Hart  and
Ziv Shami
Bradd Hart
Affiliation:
Department of Mathematics, University of Illinois at Urbana Champaign, Urbana. Illinois, USA
Ziv Shami
Affiliation:
Department of Mathematics and Statistics, Mcmaster University, Hamilton, On, Canada, E-mail: hartb@mcmaster.ca
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Abstract

Let T be simple, work in Ceq over a boundedly closed set. Let p Є S(∅) be internal in a quasi-stably-embedded type-definable set Q (e.g., Q is definable or stably-embedded) and suppose (p, Q) is ACL-embedded in Q (see definitions below). Then Aut(p/Q) with its action on pc is type-definable in Ceq over ∅. In particular, if p Є S(∅) is internal in a stably-embedded type-definable set Q, and pc ⋃ Q is stably-embedded, then Aut(p/Q) is type-definable with its action on pc.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 2 , June 2005 , pp. 379 - 388
Copyright
Copyright © Association for Symbolic Logic 2005

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References

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