Axiomatizability, the finite model property (FMP), and decidability are some of the most frequently studied properties of non-classical logics. One of the first general methods of axiomatizing large classes of superintuitionistic logics (si-logics for short) was developed by Jankov [8]. For each finite subdirectly irreducible Heyting algebra A, Jankov designed a formula that encodes the structu...

We present a category equivalent to that of semi-Nelson algebras. The objects in this are pairs consisting semi-Heyting algebra and one its filters. filters must contain all the dense elements satisfy an additional technical condition. also show case dually hemimorphic algebras, not necessary is

(6) For every finite element a of V→̇C holds {a} ∈ SubstitutionSet(V,C). (7) If A a B = A, then for every set a such that a ∈ A there exists a set b such that b ∈ B and b⊆ a. (8) If μ(A a B) = A, then for every set a such that a ∈ A there exists a set b such that b ∈ B and b⊆ a. (9) If for every set a such that a ∈ A there exists a set b such that b ∈ B and b ⊆ a, then μ(A a B) = A. Let V be a s...

In this paper we introduce a notion of dimension and codimension for every element of a distributive bounded lattice L. These notions prove to have a good behavior when L is a co-Heyting algebra. In this case the codimension gives rise to a pseudometric on L which satisfies the ultrametric triangle inequality. We prove that the Hausdorff completion of L with respect to this pseudometric is prec...

Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new s...

We answer a question [2] by Vasco Brattka and Guido Gherardi by proving that the Weihrauch lattice is not a Brouwer algebra. The computable Weihrauch lattice is also not a Heyting algebra, but the continuous Weihrauch lattice is. We further investigate embeddings of the Medvedev degrees into the Weihrauch degrees.

based on a complete heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a cartesian-closed category, calledthe category of $l-$ordered fuzzifying convergence spaces, in whichthe category of $l-$fuzzifying topological spaces can be embedded.in addition, two new categories are introduced, which are called the...