This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to...

We prove that the topology of a compact Hausdorff topological Heyting algebra is a Stone topology. It then follows from known results that a Heyting algebra is profinite iff it admits a compact Hausdorff topology that makes it a compact Hausdorff topological Heyting algebra.

ing frames O (X ) coming from a topological space to general frames is a genuine generalization of the concept of a space, as plenty of frames exist tha t are not of the form O (X ). A simple example is the frame Oreg(R) of regular open subsets of R, i.e. of open subsets U with the property ——U = U, where —U is the interior of the complement of U . This may be contrasted with the situation for ...

The variety DQD of semi-Heyting algebras with a weak negation, called dually quasi-De Morgan operation, and several of its subvarieties were investigated in the series [31], [32], [33], and [34]. In this paper we define and investigate a new subvariety JID of DQD, called “JI-distributive, dually quasi-De Morgan semi-Heyting algebras”, defined by the identity: x ∨ (y → z) ≈ (x ∨ y) → (x ∨ z), as...

Hamkins and Löwe proved that the modal logic of forcing is S4.2. In this paper, we consider its modal companion, the intermediate logic KC and relate it to the fatal Heyting algebra HZFC of forcing persistent sentences. This Heyting algebra is equationally generic for the class of fatal Heyting algebras. Motivated by these results, we further analyse the class of fatal Heyting algebras.

The determination of the injective and projective members of a category is usually a challenging problem and adds to knowledge of the category. In this paper we consider these questions for the category of Heyting algebras. There has been a lack of uniformity in terminology in recent years. In [6] Heyting algebras are referred to as pseudo-Boolean algebras, and in [1] they are called Brouwerian...

In this paper we study the structure of finitely presented Heyting algebras. Using algebraic techniques (as opposed to techniques from proof-theory) we show that every such Heyting algebra is in fact coHeyting, improving on a result of Ghilardi who showed that Heyting algebras free on a finite set of generators are co-Heyting. Along the way we give a new and simple proof of the finite model pro...

We show every monadic Heyting algebra is isomorphic to a functional monadic Heyting algebra. This solves a 1957 problem of Monteiro and Varsavsky [9].

in  cite{gl}, b. gerla and i. leuc{s}tean introduced the notion of similarity on mv-algebra. a similarity mv-algebra is an mv-algebra endowed with a binary operation $s$ that verifies certain additional properties. also, chirtec{s} in cite{c}, study the notion of similarity on l ukasiewicz-moisil algebras. in particular, strong similarity l ukasiewicz-moisil algebras were defined. in this paper...

We investigate a natural Heyting algebra structure on the set of Dyck paths of the same length. We provide a geometrical description of the operations of pseudocomplement and relative pseudocomplement, as well as of regular elements. We also find a logic-theoretic interpretation of such Heyting algebras, which we call Dyck algebras, by showing that they are the algebraic counterpart of a certai...