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 pi𝒞. 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.
Citation
Ziv Shami. "Coordinatisation by binding groups and unidimensionality in simple theories." J. Symbolic Logic 69 (4) 1221 - 1242, December 2004. https://doi.org/10.2178/jsl/1102022220
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