Interpretable groups are definable

Details Interpretable groups are definable Interpretable groups are definable

2011-10-30

arxiv.org/abs/1110.6581v1

Mathematics

Logic

Scientific paper

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.

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