Dmitry Sustretov: Generalized imaginaries and Galois cohomology


On Tuesday, November 19, we continue our seminar in Logic, Set Theory and Topology.

Please note new time and place.

Time is 10:30–12:00.

Place: Class No. 129, bldg 90

Speaker: Dmitry Sustretov (BGU)

Title: Generalized imaginaries and Galois cohomology


Given a theory T one is interested in classification (up to bi-interpretability)

of its expansions T’ with sorts internal to sorts

of T. Such expansions can be described in terms of certain definable

or type-definable groupoids, called liaison groupoids, introduced by

Hrushovski. Bi-interpetability classes of internal sorts correspond to

classes of liaison groupoids modulo certain equivalence. In this talk

I will explain how equivalence classes of connected groupoids

definable over A that trivialize over acl(A) can be described in terms

of cohomology of the Galois group Gal(acl(A)/dcl(A)). I will then

apply this correspondence to give criteria for interpretability of

“non-standard” Zariski geometries of Zilber in an algebraically closed field.


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