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Generic sets in definably compact groups

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Peterzil Y. a., Pillay A.

Fundamenta Mathematicae

2007

tom 193

nr 2

153-170

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Peterzil Y. a.

1 Pillay A.

1 2007

Wyniki wyszukiwania

Generic sets in definably compact groups