Free p-algebras revisited: An algebraic investigation of implication-free intuitionism
Tomasz Kowalski, Katarzyna Słomczyńska · Annals of Pure and Applied Logic · 2025
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.