Submission date: 30 October 2011.

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.

Mathematics Subject Classification: Primary 03C64; Secondary 03C60, 22E15, 20A15.

Keywords and phrases: o-minimality, interpretable groups, definable groups, elimination of imaginaries.

Full text arXiv 1110.6581: pdf, ps.