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Weakly one-based geometric theories

Published online by Cambridge University Press:  12 March 2014

Alexander Berenstein  and
Evgueni Vassiliev
Alexander Berenstein
Affiliation:
Universidad De Los Andes, CRA 1 NO 18A-10, Bogota, Colombia, URL: http://www.matematicas.uniandes.edu.co/˜aberenst
Evgueni Vassiliev
Affiliation:
Grenfell Campus, Memorial University of Newfoundland, Corner Brook, NL A2H 6P9, Canada, E-mail: yvasilyev@grenfell.mun.ca, URL: http://sites.google.com/site/yevgvas/
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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.

Keywords

geometric structureslinear structuresrosy theoriesgeometrieslovely pairs
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 2 , June 2012 , pp. 392 - 422
Copyright
Copyright © Association for Symbolic Logic 2012

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