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Interpretable groups are definable
Journal of Mathematical Logic 14 (1):1450002 (2014)
Abstract
We prove that in an arbitrary o-minimal structure, every interpretable group is definably isomorphic to a definable one. We also prove that every definable group lives in a cartesian product of one-dimensional definable group-intervals. We discuss the general open question of elimination of imaginaries in an o-minimal structure.Links
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2014-03-25
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2014-03-25
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Citations of this work
Interpretable sets in dense o-minimal structures.Will Johnson - 2018 - Journal of Symbolic Logic 83 (4):1477-1500.
Topologizing Interpretable Groups in p-Adically Closed Fields.Will Johnson - 2023 - Notre Dame Journal of Formal Logic 64 (4):571-609.
Orthogonal Decomposition of Definable Groups.Alessandro Berarducci, Pantelis E. Eleftheriou & Marcello Mamino - forthcoming - Journal of Symbolic Logic:1-22.
Euler characteristic of imaginaries in o-minimal structures.Sofya Kamenkovich & Ya'acov Peterzil - 2017 - Mathematical Logic Quarterly 63 (5):376-383.
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
Definably compact Abelian groups.Mário J. Edmundo & Margarita Otero - 2004 - Journal of Mathematical Logic 4 (02):163-180.
Stability in geometric theories.Jerry Gagelman - 2005 - Annals of Pure and Applied Logic 132 (2-3):313-326.
Some remarks on definable equivalence relations in o-minimal structures.Anand Pillay - 1986 - Journal of Symbolic Logic 51 (3):709-714.
Type-Definable and Invariant Groups in O-Minimal Structures.Jana Maříková - 2007 - Journal of Symbolic Logic 72 (1):67 - 80.
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