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June 2012 Weakly one-based geometric theories
Alexander Berenstein, Evgueni Vassiliev
J. Symbolic Logic 77(2): 392-422 (June 2012). DOI: 10.2178/jsl/1333566629

Abstract

We study the class of weakly locally modular geometric theories introduced in [4], a common generalization of the classes of linear SU-rank 1 and linear o-minimal theories. We find new conditions equivalent to weak local modularity: “weak one-basedness”, absence of type definable “almost quasidesigns”, and “generic linearity”. Among other things, we show that weak one-basedness is closed under reducts. We also show that the lovely pair expansion of a non-trivial weakly one-based ω-categorical geometric theory interprets an infinite vector space over a finite field.

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Alexander Berenstein. Evgueni Vassiliev. "Weakly one-based geometric theories." J. Symbolic Logic 77 (2) 392 - 422, June 2012. https://doi.org/10.2178/jsl/1333566629

Information

Published: June 2012
First available in Project Euclid: 4 April 2012

zbMATH: 06047768
MathSciNet: MR2963013
Digital Object Identifier: 10.2178/jsl/1333566629

Subjects:
Primary: 03C45, 03C64

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 2 • June 2012
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