Interpretable groups are definable
Department of Mathematics and Statistics, University of Konstanz, Zukunftskolleg, Box 216, 78457 Konstanz, Germany
Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel
Google, Inc., 76 9th Ave, New York, NY 10011, USA
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.



