Generic sets in definably compact groups

• Autorzy: Ya'acov Peterzil , Anand Pillay
• Języki publikacji: EN

Abstrakty

EN

A subset X of a group G is called left genericif 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.

Kategorie tematyczne

• 03C64: Model theory of ordered structures; o-minimality
• 22E15: General properties and structure of real Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 193
• Numer: 2
• Strony: 153-170

Daty

wydano

2007

Twórcy

autor

Ya'acov Peterzil

• Department of Mathematics, University of Haifa, Haifa, Israel

autor

Anand Pillay

• Department of Mathematics, UIUC, Urbana, IL 61801, U.S.A.
• School of Mathematics, University of Leeds, Leeds LS2 9JT, UK

Identyfikatory

DOI

10.4064/fm193-2-4