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Coordinatisation by binding groups and unidimensionality in simple theories

Published online by Cambridge University Press:  12 March 2014

Ziv Shami
Ziv Shami*
Affiliation:
Department of Mathematics, University of Illinoisat Urbana Champaign, USA, E-mail: [email protected]
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Abstract.

In a simple theory with elimination of finitary hyperimaginaries if tp(a) is real and analysable over a definable set Q, then there exists a finite sequence (ai \ i ≤ n*) ⊆ dcleq(a) with an* = a such that for every i ≤ n* if pi = tp(ai/{aj |j < i}) then Aut(pi / Q) is type-definable with its action on . A unidimensional simple theory eliminates the quantifier ∃∞ and either interprets (in Ceq) an infinite type-definable group or has the property that ACL(Q) = C for every infinite definable set Q.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 4 , December 2004 , pp. 1221 - 1242
Copyright
Copyright © Association for Symbolic Logic 2004

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References

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