On analyzability in the forking topology for simple theories

Annals of Pure and Applied Logic 142 (1):115-124 (2006)

Abstract

We show that in a simple theory T in which the τf-topologies are closed under projections every type analyzable in a supersimple τf-open set has ordinal SU-rank. In particular, if in addition T is unidimensional, the existence of a supersimple unbounded τf-open set implies T is supersimple. We also introduce the notion of a standard τ-metric and show that for simple theories its completeness is equivalent to the compactness of the τ-topology

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References found in this work

Lovely Pairs of Models.Itay Ben-Yaacov, Anand Pillay & Evgueni Vassiliev - 2003 - Annals of Pure and Applied Logic 122 (1-3):235-261.
Lascar Strong Types in Some Simple Theories.Steven Buechler - 1999 - Journal of Symbolic Logic 64 (2):817-824.
Definability in Low Simple Theories.Ziv Shami - 2000 - Journal of Symbolic Logic 65 (4):1481-1490.
Internality and Interpretable Automorphism Groups in Simple Theories.Ziv Shami - 2004 - Annals of Pure and Applied Logic 129 (1-3):149-162.

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Citations of this work

On the Forking Topology of a Reduct of a Simple Theory.Ziv Shami - 2020 - Archive for Mathematical Logic 59 (3-4):313-324.
On Uncountable Hypersimple Unidimensional Theories.Ziv Shami - 2014 - Archive for Mathematical Logic 53 (1-2):203-210.
A Note on the Non‐Forking‐Instances Topology.Ziv Shami - 2020 - Mathematical Logic Quarterly 66 (3):336-340.
Continuity of SU-Rank in Unidimensional Supersimple Theories.Ziv Shami - 2016 - Archive for Mathematical Logic 55 (5-6):663-675.

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