Locally definable subgroups of semialgebraic groups

Elías Baro, Pantelis E. Eleftheriou, Ya’acov Peterzil

Type: Article

Publication Date: 2019-10-07

Citations: 1

DOI: https://doi.org/10.1142/s0219061320500099

Abstract

We prove the following instance of a conjecture stated in [P. E. Eleftheriou and Y. Peterzil, Definable quotients of locally definable groups, Selecta Math. (N.S.) 18(4) (2012) 885–903]. Let [Formula: see text] be an abelian semialgebraic group over a real closed field [Formula: see text] and let [Formula: see text] be a semialgebraic subset of [Formula: see text]. Then the group generated by [Formula: see text] contains a generic set and, if connected, it is divisible. More generally, the same result holds when [Formula: see text] is definable in any o-minimal expansion of [Formula: see text] which is elementarily equivalent to [Formula: see text]. We observe that the above statement is equivalent to saying: there exists an [Formula: see text] such that [Formula: see text] is an approximate subgroup of [Formula: see text].

Locations

Journal of Mathematical Logic - View
arXiv (Cornell University) - View - PDF

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