English

Interpretable groups are definable

Logic 2011-11-01 v1

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.

Keywords

Cite

@article{arxiv.1110.6581,
  title  = {Interpretable groups are definable},
  author = {Janak Ramakrishnan and Ya'acov Peterzil and Pantelis Eleftheriou},
  journal= {arXiv preprint arXiv:1110.6581},
  year   = {2011}
}
R2 v1 2026-06-21T19:27:58.825Z