Decidability and finite axiomatizability of theories of ℵ0-categorical partially ordered sets
James H. Schmerl · Journal of Symbolic Logic · 1981
Abstract Every ℵ0-categorical partially ordered set of finite width has a finitely axiomatizable theory. Every ℵ0-categorical partially ordered set of finite weak width has a decidable theory. This last statement constitutes a major portion of the complete (with three exceptions) characterization of those finite partially ordered sets for which any ℵ0-categorical partially ordered set not embedding one of them has a decidable theory.