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On the Type-Definability of the Binding Group in Simple Theories
Bradd Hart and Ziv Shami
The Journal of Symbolic Logic
Vol. 70, No. 2 (Jun., 2005), pp. 379-388
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/27588368
Page Count: 10
You can always find the topics here!Topics: Equivalence relation, Automorphisms, Indiscernibles, Logical theorems, Definable sets, Mathematics
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Let T be simple, work in Ceq over a boundedly closed set. Let p ∈ S(θ) 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 θ. In particular, if p ∈ S(θ) is internal in a stably-embedded type-definable set Q, and pC υ Q is stably-embedded, then Aut(p/Q) is type-definable with its action on pC.
The Journal of Symbolic Logic © 2005 Association for Symbolic Logic