Preservation under Reduced Products in Continuous Logic

Abstract

We introduce a fragment of continuous first-order logic, analogue of Palyutin formulas (or h-formulas) in classical model theory, which is preserved under reduced products in both directions. We use it to extend classical results on complete theories which are preserved under reduced product and their stability. We also characterize the set of Palyutin sentences, Palyutin theories and other related fragments in terms of their preservation properties, both in the classical setting and the metric one.