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.

Abstract We construct the finitely generated free algebras and determine the free spectra of varieties of linear equivalential algebras and linear equivalential algebras of finite height corresponding, respectively, to the equivalential fragments of intermediate Gödel-Dummett logic and intermediate finite-valued logics of Gödel. Thus we compute the number of purely equivalential propositional formulas in these logics in n variables for an arbitrary n ∈ ℕ.