  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.
