Supersimple theories enlarged with a dense independent subset

par Alexander Berenstein (Los Andes)

mardi 14 juin 2016, 14:30 → 15:30 Europe/Paris

ICJ, salle séminaire 2, bât. Braconnier, UCBL - La Doua

Let T be a geometric theory, that is, a theory that eliminates the quantifier exists^infinity and such that in every model of the theory, the algebraic closure satisfies the exchange property.
An H-structure associated to T is an expansion of a model M of T by a predicate P of algebraically independent elements which is dense and codense: every non-algebraic 1-type p(x) has a realization in P and a realization independent from P.
In this talk we will introduce H-structures and some of their properties. We will also extend the definition to the supersimple setting and show that the theory of such pairs is again supersimple.

(joint work with J.F. Carmona and E. Vassiliev)