Abstract We introduce prime products as a generalization of ultraproducts for positive logic. Prime products are shown to satisfy a version of Łoś’s Theorem restricted to positive formulas, as well as the following variant of the Keisler Isomorphism Theorem: under the generalized continuum hypothesis, two models have the same positive theory if and only if they have isomorphic prime powers of ultrapowers.

Abstract Roelcke non-precompactness, simplicity, and non-amenability of the automorphism group of the Fraïssé limit of finite Heyting algebras are proved among others.

This article presents results in modal correspondence theory for possibility semantics, a generalization of Kripke semantics introduced by Humberstone and later developed by Holliday and others. First, it is shown by an algebraic argument that all Sahlqvist formulae have first-order correspondents over possibility frames. Second, model-theoretic aspects of correspondence over possibility frames are examined in the style of van Benthem.