On the universal theory of the free pseudocomplemented distributive lattice

Articolo

Data di Pubblicazione:

2025

Citazione:

On the universal theory of the free pseudocomplemented distributive lattice / L. Carai, T. Moraschini. - In: JOURNAL OF ALGEBRA. - ISSN 1090-266X. - 682:(2025 Nov 15), pp. 634-671. [10.1016/j.jalgebra.2025.05.043]

Abstract:

It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of the full elementary theory of the finitely generated free algebras which is known to be undecidable. As a by-product, a description of the finitely generated pseudocomplemented distributive lattices that can be embedded into the free algebra is also obtained.

Tipologia IRIS:

01 - Articolo su periodico

Keywords:

Admissible rule; Decidability; Duality theory; Esakia space; Free algebra; Free skeleton; Heyting algebra; Intuitionistic logic; p-algebra; Priestley space; Pseudocomplemented distributive lattice; Universal theory;

Elenco autori: