Free p-algebras revisited: an algebraic investigation of implication-free intuitionism
Tomasz Kowalski, Katarzyna S{\l}omczy\'nska
TL;DR
This paper presents a new universal algebraic construction of free distributive p-algebras, providing a normal form theorem, simplified proofs, and a complete characterization of structurally complete varieties, advancing the algebraic understanding of implication-free intuitionism.
Contribution
It introduces a novel algebraic construction relying on meet-irreducible congruences, simplifying existing results and characterizing structurally complete p-algebra varieties.
Findings
A new universal algebraic construction of free distributive p-algebras.
A normal form theorem for p-algebra terms.
Complete characterization of structurally complete p-algebra varieties.
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 well as a complete characterisation of structurally complete varieties of p-algebras.
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Taxonomy
TopicsAdvanced Algebra and Logic · Logic, Reasoning, and Knowledge · Advanced Topology and Set Theory