Modular types in some supersimple theories

Journal of Symbolic Logic 67 (4):1601-1615 (2002)
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Abstract

We consider a small supersimple theory with a property (CS) (close to stability). We prove that if in such a theoryTthere is a typep∈S(A) (whereAis finite) withSU(p) = 1 and infinitely many extensions overacleq(A), then inTthere is a modular such type. Also, ifTis supersimple with (CS) andp∈S(∅) is isolated,SU(p) = 1 andphas infinitely many extensions overacleq(∅), thenpis modular.

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10.2178/jsl/1190150302

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References found in this work

Simple theories.Byunghan Kim & Anand Pillay - 1997 - Annals of Pure and Applied Logic 88 (2-3):149-164.
ℵ0-Categorical, ℵ0-stable structures.Gregory Cherlin, Leo Harrington & Alistair H. Lachlan - 1985 - Annals of Pure and Applied Logic 28 (2):103-135.
Meager forking.Ludomir Newelski - 1994 - Annals of Pure and Applied Logic 70 (2):141-175.
Simple unstable theories.Saharon Shelah - 1980 - Annals of Mathematical Logic 19 (3):177.

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