Grigory Mashevitzky: On the action of endomorphisms of an algebra A on the definable subsets over A

Tuesday, June 11, we continue our seminar in Logic, Set Theory and Topology.

Time is 16:00 – 17:30.

Place: seminar room 201 of Mathematics Department.

Speaker: Mashevitzky Grigory (BGU)
Title: On the action of endomorphisms of an algebra A on the definable subsets over A.
Abstract: The aim of this talk is to construct and discuss the Galois type correspondence between subsemigroups of the transformation semigroup,
in particular the endomorphism semigroup, of an algebra and special subsets in the algebra of first order formulas.
I discuss some possible applications of this correspondence.
It can be applied for recognizing definable sets which can be defined by formulas of a reduct of an original language )
i.e. formulas constructed with the help of a restricted set of operations, predicates and logical operations).
As the second possible application I suggest a ladder for the homogeneity properties of models and its applications.
The unification types theory consider the special method of describing solutions of equations over algebras.

The third application concerns the generalization of the unification theory to the logic unification theory

(which consider the special method of describing definable sets) and the topology approach to the logic unification types theory.

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