Interpretable groups are definable

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number1450002
JournalJournal of Mathematical Logic
Issue number1
StatePublished - 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).


  • definable groups
  • elimination of imaginaries
  • interpretable groups
  • o-minimality

ASJC Scopus subject areas

  • Logic


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