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.
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]
On the universal theory of the free pseudocomplemented distributive lattice
L. CaraiPrimo
;
2025
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.
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