Finiteness of U-rank implies simplicity in homogeneous structures

Mathematical Logic Quarterly 49 (6):576 (2003)
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Abstract

A superstable homogeneous structure is said to be simple if every complete type over any set A has a free extension over any B ⊇ A. In this paper we give a characterization for this property in terms of U-rank. As a corollary we get that if the structure has finite U-rank, then it is simple

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10.1002/malq.200310062

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Citations of this work

Quasiminimal structures, groups and Zariski-like geometries.Tapani Hyttinen & Kaisa Kangas - 2016 - Annals of Pure and Applied Logic 167 (6):457-505.
Simplicity and uncountable categoricity in excellent classes.Tapani Hyttinen & Olivier Lessmann - 2006 - Annals of Pure and Applied Logic 139 (1):110-137.
Canonical bases in excellent classes.Tapani Hyttinen & Olivier Lessmann - 2008 - Journal of Symbolic Logic 73 (1):165-180.

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Strong splitting in stable homogeneous models.Tapani Hyttinen & Saharon Shelah - 2000 - Annals of Pure and Applied Logic 103 (1-3):201-228.

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