On the universal theory of the free pseudocomplemented distributive lattice
Logic
2025-07-15 v2
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.
Keywords
Cite
@article{arxiv.2409.03640,
title = {On the universal theory of the free pseudocomplemented distributive lattice},
author = {Luca Carai and Tommaso Moraschini},
journal= {arXiv preprint arXiv:2409.03640},
year = {2025}
}