Structures with Two Partial Orders and the Amalgamation Property

Abstract

We show that partially ordered sets, lattices, semilattices, Boolean algebras, Heyting algebras with a further coarser or finer partial order, or a linearization, or an auxiliary relation have the strong amalgamation property, Fraïssé limits and, in many cases, an \(\omega\)-categorical model completion with quantifier elimination. The same applies to causal spaces, introduced by Kronheimer and Penrose in connection with foundational problems in general relativity. Our main tool is the superamalgamation property, thus we provide arguments suggesting the usefulness of the superamalgamation property also in pure model theory, not only in algebraic logic.