Dominions in Filtral Quasivarieties

CAMPERCHOLI, MIGUEL

Praga

Congreso; Logic Colloquium 2019; 2019

Association for Symbolic Logic

In our talk we shall present the following result and discuss some of its applications.Theorem: Let Q be a filtral quasivariety abd let M be its class of simple members. Suppose M has the amalgamation propoerty and that M_ec (the class of existentially closed structures in M) is axiomatizable. Then, for all B in Q, every A in S(B), and every b in B the following are equivalent:- b is in the domonion of A in B relative to Q.- There is a conjunction of atomic formulas D(x1,...xn,y) and a1,...,an in A such that D(x1,...xn,y) defines a function in Q and B satisfies D(a1,...,an,b).