Interpretable groups are definable

2011/10/30 by Ramakrishnan, Janak, Peterzil, Ya'acov, Eleftheriou, Pantelis
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1110.6581

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.

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