locally definable groups
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2019 ◽  
Vol 20 (02) ◽  
pp. 2050009
Author(s):  
Elías Baro ◽  
Pantelis E. Eleftheriou ◽  
Ya’acov Peterzil

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].



2013 ◽  
Vol 19 (3) ◽  
pp. 719-736 ◽  
Author(s):  
Alessandro Berarducci ◽  
Mário Edmundo ◽  
Marcello Mamino


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


2008 ◽  
Vol 320 (7) ◽  
pp. 3079-3080 ◽  
Author(s):  
Elías Baro ◽  
Mário J. Edmundo


2006 ◽  
Vol 301 (1) ◽  
pp. 194-223 ◽  
Author(s):  
Mário J. Edmundo


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