Interpretable groups are definable

Pantelis E. Eleftheriou; Ya'Acov Peterzil; Janak Ramakrishnan

doi:10.1142/S0219061314500020

Interpretable groups are definable

Pantelis E. Eleftheriou, Ya'Acov Peterzil, Janak Ramakrishnan

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 (or one-dimensional definable groups). We discuss the general open question of elimination of imaginaries in an o-minimal structure.

Original language	English
Article number	1450002
Journal	Journal of Mathematical Logic
Volume	14
Issue number	1
DOIs	https://doi.org/10.1142/S0219061314500020
State	Published - Jun 2014

Bibliographical note

Funding Information:
The authors thank Mário Edmundo and the FCT grant PTDC/MAT/101740/2008 for bringing them together in Lisbon, where this work was begun. They also thank the referee for the careful reading of the paper. The first author is supported by the EU FP7 Marie Curie Zukunftskolleg Incoming Fellowship Programme, University of Konstanz (grant no. 291784).

Keywords

definable groups
elimination of imaginaries
interpretable groups
o-minimality

ASJC Scopus subject areas

Logic

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10.1142/S0219061314500020

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AU - Ramakrishnan, Janak

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AB - 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 (or one-dimensional definable groups). We discuss the general open question of elimination of imaginaries in an o-minimal structure.

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ER -

Interpretable groups are definable

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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