Journal of Symbolic Logic 69 (4):1221 - 1242 (2004)

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 ( $a_{i}|i \leq n^{*}$ ) $\subseteq dcl^{eq}$ (a) with $a_{n}*$ = a such that for every $i \leq n*$ , if $p_{i} = tp(a_{i}/{a_{i}|j < i}$ ) then $Aut(p_{i}/Q)$ is type-definable with its action on $p_{i}^{c}$ . A unidimensional simple theory eliminates the quantifier $\exists^{\infty}$ and either interprets (in $C^{eq}$ ) an infinite type-definable group or has the property that ACL(Q) = C for every infinite definable set Q
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DOI 10.2178/jsl/1102022220
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References found in this work BETA

Simple Theories.Byunghan Kim & Anand Pillay - 1996 - Annals of Pure and Applied Logic 88 (2):149-164.
Unidimensional Theories Are Superstable.Ehud Hrushovski - 1990 - Annals of Pure and Applied Logic 50 (2):117-137.
Internality and Interpretable Automorphism Groups in Simple Theories.Ziv Shami - 2004 - Annals of Pure and Applied Logic 129 (1-3):149-162.
Simple Unstable Theories.Saharon Shelah - 1980 - Annals of Pure and Applied Logic 19 (3):177.
Unidimensional Theories Are Superstable.Katsuya Eda - 1990 - Annals of Pure and Applied Logic 50 (2):117-137.

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Citations of this work BETA

On Analyzability in the Forking Topology for Simple Theories.Ziv Shami - 2006 - Annals of Pure and Applied Logic 142 (1):115-124.
On Uncountable Hypersimple Unidimensional Theories.Ziv Shami - 2014 - Archive for Mathematical Logic 53 (1-2):203-210.
On Countable Simple Unidimensional Theories.Anand Pillay - 2003 - Journal of Symbolic Logic 68 (4):1377-1384.
Continuity of SU-Rank in Unidimensional Supersimple Theories.Ziv Shami - 2016 - Archive for Mathematical Logic 55 (5-6):663-675.

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