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Invariance results for definable extensions of groups
Archive for Mathematical Logic 50 (1-2):19-31 (2011)
Abstract
We show that in an o-minimal expansion of an ordered group finite definable extensions of a definable group which is defined in a reduct are already defined in the reduct. A similar result is proved for finite topological extensions of definable groups defined in o-minimal expansions of the ordered set of real numbers.Author's Profile
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Citations of this work
Fundamental group in o-minimal structures with definable Skolem functions.Bruno Dinis, Mário J. Edmundo & Marcello Mamino - 2021 - Annals of Pure and Applied Logic 172 (8):102975.
References found in this work
Type-definability, compact lie groups, and o-minimality.Anand Pillay - 2004 - Journal of Mathematical Logic 4 (02):147-162.
Definably compact Abelian groups.Mário J. Edmundo & Margarita Otero - 2004 - Journal of Mathematical Logic 4 (02):163-180.
Definable homomorphisms of abelian groups in o-minimal structures.Ya'acov Peterzil & Sergei Starchenko - 1999 - Annals of Pure and Applied Logic 101 (1):1-27.
Groups Definable in Ordered Vector Spaces over Ordered Division Rings.Pantelis E. Eleftheriou & Sergei Starchenko - 2007 - Journal of Symbolic Logic 72 (4):1108 - 1140.
The universal covering homomorphism in o‐minimal expansions of groups.Mário J. Edmundo & Pantelis E. Eleftheriou - 2007 - Mathematical Logic Quarterly 53 (6):571-582.
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