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Interpretable groups are definable
Pantelis Eleftheriou
Ya'acov Peterzil
Journal of Mathematical Logic, vol. 14 (2014)
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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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We show, for various classes of totally ordered structures \mathcal M=(M,<,...), including o-minimal and weakly o-minimal structures, that every definable partial order on a subset of M^n extends definably in \mathcal M to a total order. This extends the result proved in [5] for n=1 and  \mathcal M o-minimal.
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Definable functions continuous on curves in o-minimal structures
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Annals of Pure and Applied Logic, vol. 165 (2014), pp. 1339-1351
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