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Journal of Mathematical Logic: Vol. 14, No. 01
Print ISSN: 0219-0613
Online ISSN: 1793-6691

 
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Interpretable groups are definable

Pantelis E. Eleftheriou

Department of Mathematics and Statistics, University of Konstanz, Zukunftskolleg, Box 216, 78457 Konstanz, Germany

Ya'acov Peterzil

Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel

Janak Ramakrishnan

Google, Inc., 76 9th Ave, New York, NY 10011, USA

Received: 4 March 2012
Accepted: 1 March 2014
Published: 14 May 2014

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.

Keywords: o-minimality; interpretable groups; definable groups; elimination of imaginaries
AMSC: Primary: 03C64, Secondary: 03C60, Secondary: 22E15, Secondary: 20A15
Cited by (1):
. (2016) Linearity of groups definable in o-minimal structures. Selecta Mathematica. Online publication date: 8-Jul-2016. [CrossRef]