Generic sets in definably compact groups

Ya'acov Peterzil, and Anand Pillay. "Generic sets in definably compact groups." Fundamenta Mathematicae 193.2 (2007): 153-170. <http://eudml.org/doc/286617>.

@article{YaacovPeterzil2007,
abstract = { 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. },
author = {Ya'acov Peterzil, Anand Pillay},
journal = {Fundamenta Mathematicae},
keywords = {o-minimal structure; definably compact group; generic set; Haar measure; forking},
language = {eng},
number = {2},
pages = {153-170},
title = {Generic sets in definably compact groups},
url = {http://eudml.org/doc/286617},
volume = {193},
year = {2007},
}

TY - JOUR
AU - Ya'acov Peterzil
AU - Anand Pillay
TI - Generic sets in definably compact groups
JO - Fundamenta Mathematicae
PY - 2007
VL - 193
IS - 2
SP - 153
EP - 170
AB - 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.
LA - eng
KW - o-minimal structure; definably compact group; generic set; Haar measure; forking
UR - http://eudml.org/doc/286617
ER -