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SUMMARY:Amador Martin-Pizarro - Stability and the strong Erdős-Hajnal pro
 perty
DTSTART:20260521T120000Z
DTEND:20260521T130000Z
DTSTAMP:20260614T000300Z
UID:indico-event-16620@indico.math.cnrs.fr
DESCRIPTION:Abstract. A bipartite graph R on U x V has the strong Erdős-H
 ajnal Property if there exits a constant delta>0 such that for any finite 
 subsets A of U and B of V\, there exists an R-homogeneous pair (A_0\, B_0)
 \, where A_0\, resp. B_0\, is a subset of A\, resp. of B\, of relative den
 sity at least delta.Chernikov and Starchenko showed that every bipartite g
 raph definable in a distal theory has the strong Erdős-Hajnal Property. S
 table theories cannot be distal (but many relevant stable theories are red
 ucts of distal theories\, and thus inherit the strong Erdős-Hajnal Proper
 ty). In this talk\, we will present an elementary proof of the strong Erd
 ős-Hajnal Property for a certain class of stable theories.\n\nhttps://ind
 ico.math.cnrs.fr/event/16620/
LOCATION:112 (ICJ)
URL:https://indico.math.cnrs.fr/event/16620/
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