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

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 semilatttice and the poset of join-irreducibles of the free p-algebra augmented by zero.