Description of positively existentially closed models in any class of -structures with unary predicates axiomatizable by any h-universal sentence.

Abstract

It was shown that any finitely h-universally axiomatized class of models in unary predicate signature has a finite number of positively existentially closed models, and all them are finite. Proposed the example of a class of models which described by the infinite number of h-universal sentences and its class of positively existential closed models is not elementary.