Locally definable subgroups of semialgebraic groups

Eliás Baro, Pantelis E. Eleftheriou, Ya'acov Peterzil

Research output: Contribution to journalArticlepeer-review

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 G be an abelian semialgebraic group over a real closed field R and let X be a semialgebraic subset of G. Then the group generated by X contains a generic set and, if connected, it is divisible. More generally, the same result holds when X is definable in any o-minimal expansion of R which is elementarily equivalent to a an,exp. We observe that the above statement is equivalent to saying: there exists an m such that ςi=1m(X - X) is an approximate subgroup of G.

Original languageAmerican English
Article number2
Pages (from-to)2050009:1-2050009:17
Number of pages17
JournalJournal of Mathematical Logic
Volume20
Issue number2
DOIs
StatePublished - 1 Aug 2020

Keywords

  • Semialgebraic groups
  • approximate groups
  • generic sets
  • lattices
  • locally definable groups

All Science Journal Classification (ASJC) codes

  • Logic

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