Positive Primitive Structures

We investigate a positive primitive formula closure (formed by (exist,&,=)-formulas) in countable structures which establishes an algebraic framework for Constraint Satisfaction Problems on a countable set. The main question under consideration is the characterization of countable structures, called positive primitive, in which, similar to a finite case, such closure coincides with the Galois closure on predicates invariant to all polymorphisms of those structures. Next we establish criteria for existential quantifier elimination in positive primitive formulas.