Generic sets in definably compact groups

Ya'acov Peterzil, Anand Pillay

Research output: Contribution to journalArticlepeer-review


A subset X of a group G is called left generic if finitely many left translates of X cover G. Our main result is that if G is a definably compact group in an o-minimal structure and a definable X ⊆ G is not right generic then its complement is left generic. Among our additional results are (i) a new condition equivalent to definable compactness, (ii) the existence of a finitely additive invariant measure on definable sets in a definably compact group G in the case where G = *H for some compact Lie group H (generalizing results from [1]), and (iii) in a definably compact group every definable subsemi-group is a subgroup. Our main result uses recent work of Alf Dolich on forking in o-minimal stuctures.

Original languageEnglish
Pages (from-to)153-170
Number of pages18
JournalFundamenta Mathematicae
Issue number2
StatePublished - 2007


  • Definably compact group
  • Forking
  • Generic set
  • Haar measure
  • O-minimal structure

ASJC Scopus subject areas

  • Algebra and Number Theory


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