Adding ultrafilters by definable quotients

2011 ◽  
Vol 60 (3) ◽  
pp. 445-454 ◽  
Author(s):  
Michael Hrušák ◽  
Jonathan L. Verner
Keyword(s):  
Definable Quotients

TOPOLOGICAL DYNAMICS OF STABLE GROUPS

2014 ◽  
Vol 79 (4) ◽  
pp. 1199-1223 ◽  
Author(s):  
LUDOMIR NEWELSKI
Keyword(s):  
Inverse Limit ◽  
Topological Dynamics ◽  
Maximal Subgroups ◽  
Inverse Limits ◽  
Stable Theory ◽  
Definable Quotients

AbstractAssumeGis a group definable in a modelMof a stable theoryT. We prove that the semigroupSG(M) of completeG-types overMis an inverse limit of some semigroups type-definable inMeq. We prove that the maximal subgroups ofSG(M) are inverse limits of some definable quotients of subgroups ofG. We consider the powers of types in the semigroupSG(M) and prove that in a way every type inSG(M) is profinitely many steps away from a type in a subgroup ofSG(M).

scholarly journals Locally definable subgroups of semialgebraic groups

2019 ◽  
Vol 20 (02) ◽  
pp. 2050009
Author(s):  
Elías Baro ◽  
Pantelis E. Eleftheriou ◽  
Ya’acov Peterzil
Keyword(s):  
Real Closed Field ◽  
Closed Field ◽  
Definable Groups ◽  
Locally Definable Groups ◽  
Semialgebraic Subset ◽  
Generic Set ◽  
Definable Quotients

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 [Formula: see text] be an abelian semialgebraic group over a real closed field [Formula: see text] and let [Formula: see text] be a semialgebraic subset of [Formula: see text]. Then the group generated by [Formula: see text] contains a generic set and, if connected, it is divisible. More generally, the same result holds when [Formula: see text] is definable in any o-minimal expansion of [Formula: see text] which is elementarily equivalent to [Formula: see text]. We observe that the above statement is equivalent to saying: there exists an [Formula: see text] such that [Formula: see text] is an approximate subgroup of [Formula: see text].

scholarly journals Definable quotients of locally definable groups

2012 ◽  
Vol 18 (4) ◽  
pp. 885-903 ◽  
Author(s):  
Pantelis E. Eleftheriou ◽  
Ya’acov Peterzil
Keyword(s):  
Definable Groups ◽  
Locally Definable Groups ◽  
Definable Quotients
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