Work

Free p-algebras revisited: An algebraic investigation of implication-free intuitionism

Year: 2025

Type: article

Abstract: We give a new construction of free distributive p-algebras. Our construction relies on a detailed description of completely meet-irreducible congruences, so it is purely universal algebraic. It yields a normal form theorem for p-algebra terms, simpler proofs of several existing results. As a by-product, we obtain an isomorphism between the free pseudocomplemented semilattice and the poset of join-irreducibles of the free p-algebra augmented by zero.

Source: Annals of Pure and Applied Logic

DOI: 10.1016/j.apal.2025.103610

Authors: Tomasz Kowalski, Katarzyna Słomczyńska

Institutions: Jagiellonian University, The University of Queensland, La Trobe University, Uniwersytet Komisji Edukacji Narodowej w Krakowie

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,520

Funder: Narodowe Centrum Nauki