Algebraic semantics for the ‐fragment of and its properties

Abstract

We study the variety of equivalential algebras with zero and its subquasivariety that gives the equivalent algebraic semantics for the (↔,¬)‐fragment of intuitionistic propositional logic. We prove that this fragment is hereditarily structurally complete. Moreover, we effectively construct the finitely generated free equivalential algebras with zero.

The structure of completely meet irreducible congruences in strongly Fregean algebras

“…In [13] and [9] we used this relation in the set of join irreducible elements of congruence lattices of finite algebras from congruence permutable Fregean varieties to understand their structure. However, in a series of papers [14], [15] and [16] we apply the same relation, but this time in the set of completely meet irreducible elements of congruence lattice, in particular, to construct free algebras in the varieties under consideration. This perspective is, in a sense, dual to the former, though substantially different, since the posets of join and meet irreducible elements of the congruence lattice need not to be isomorphic, and the latter approach can be applied also in the infinite case, in contrast to the former one.…”