Via the introduction of (infinitary) disjunctions on any complete lattice while inheriting the meet as a conjunction, we construct a bijective correspondence (up to isomorphism) between complete lattices L and complete Heyting algebras DI(L) equipped with a so called disjunctive join dense closure operator RL. If L is itself a complete Heyting algebra then DI(L) ∼= L and RL = idDI(L). Ortholatt...

The Semi Heyting Almost Distributive Lattice (SHADL) is a mathematical framework that combines the concepts of semi algebra and almost distributive lattice. This abstract highlights applications SHADL in various domains

This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, that the variety $mathbf{RDQDStSH_1}$ of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{RDQDStSH_1}$-chains and the variety of dually quasi-De Morgan Boolean semi-Heyting algebras--...

The provision of ontologies for spatial entities is an important topic in spatial information theory. Heyting algebras, co-Heyting algebras, and bi-Heyting algebras are structures having considerable potential for the theoretical basis of these ontologies. This paper gives an introduction to these Heyting structures, and provides evidence of their importance as algebraic theories of sets of reg...

We show that for a variety V of Heyting algebras the following conditions are equivalent: (1) V is locally finite; (2) the V-coproduct of any two finite V-algebras is finite; (3) either V coincides with the variety of Boolean algebras or finite V-copowers of the three element chain 3 ∈ V are finite. We also show that a variety V of Heyting algebras is generated by its finite members if, and onl...

based on a complete heyting algebra l, the relations between lfuzzifyingconvergence spaces and l-fuzzifying topological spaces are studied.it is shown that, as a reflective subcategory, the category of l-fuzzifying topologicalspaces could be embedded in the category of l-fuzzifying convergencespaces and the latter is cartesian closed. also the specialization l-preorderof l-fuzzifying convergenc...

The appearance of the complete Heyting algebra in the realm of Algebraic Topology is the main topic of the paper.

It is well-known that any substitution in intuitionistic propositional logic can be seen as an endomorphism between free Heyting algebras. For a given substitution σ : F (n)→ F (m), (where F (n) is the n-generated free Heyting algebra, n ∈ ω), the theory of σ is the filter σ−1(>). The theory of σ is finitely axiomatizable if σ−1(>) is a principal filter. The formula which generates this filter ...

In this paper we investigate various properties of equivalence classes of fuzzy equivalence relations over a complete residuated lattice. We give certain characterizations of fuzzy semipartitions and fuzzy partitions over a complete residuated lattice, as well as over a linearly ordered complete Heyting algebra. In the latter case, for a fuzzy equivalence relation over a linearly ordered comple...