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SUMMARY:H-structures
DTSTART;VALUE=DATE-TIME:20191003T083000Z
DTEND;VALUE=DATE-TIME:20191003T093000Z
DTSTAMP;VALUE=DATE-TIME:20191015T234500Z
UID:indico-event-5079@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexander Berenstein (Universidad de los Andes)\n\n\
n\nAbstract: A complete theory T is called geometric if the algebraic clos
ure has the exchange property in all models of T and thetheory eliminates
the quantifier exists infinity. In such theories there is a rudimentary no
tion of independence given by algebraic independence. Examples of geometri
c theories include SU-rank one theories and dense o-minimal theories.\nAn
expansion of a model M of T by a unary predicate H is called dense-codense
if for every finite dimensional subset A of M and every non algebraic typ
e p(x) over A\, there is a realization of p(x) in H(M) and another one whi
ch is not algebraic over AH(M).A dense-codense expansion is called an H-st
ructure if in addition H(M) is algebraically independent.\n\nIn this talk
we will talk about the basic properties of H-structures and explain why th
e new structure can be understood as a tame expansion of the original stru
cture M. We will discuss groups definable in this expansion. We will also
present some recent results on the special case when M is the ultrapower o
f a one-dimensional asymptotic class.\n\nThis talk includes joint work wit
h E. Vassiliev\, D. Garcia and T. Zou.\nhttps://indico.math.cnrs.fr/event/
5079/
LOCATION:112 (Braconnier)
URL:https://indico.math.cnrs.fr/event/5079/
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