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.
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}
}