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Non-standard lattices and o-minimal groups

Published online by Cambridge University Press:  05 September 2014

Pantelis E. Eleftheriou
Pantelis E. Eleftheriou*
Affiliation:
University of Waterloo, Department of Pure Mathematics, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada E-mail: pelefthe@uwaterloo.ca
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Abstract

We describe a recent program from the study of definable groups in certain o-minimal structures. A central notion of this program is that of a (geometric) lattice. We propose a definition of a lattice in an arbitrary first-order structure. We then use it to describe, uniformly, various structure theorems for o-minimal groups, each time recovering a lattice that captures some significant invariant of the group at hand. The analysis first goes through a local level, where a pertinent notion of pregeometry and generic elements is each time introduced.

Keywords

03C6403C68O-minimalitynon-standard lattices-definable groups
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 19 , Issue 1 , March 2013 , pp. 56 - 76
Copyright
Copyright © Association for Symbolic Logic 2013

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