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Preprint Number 370
370. Pantelis E. Eleftheriou, Ya'acov Peterzil and Janak Ramakrishnan
Interpretable groups are definable
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Submission date: 30 October 2011.
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.
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