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

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...

We study Nonassociative Lambek Calculus with additives ∧,∨, satisfying the distributive law (Full Nonassociative Lambek Calculus with Distribution DFNL). We prove that formal grammars based on DFNL, also with assumptions, generate context-free languages. The proof uses proof-theoretic tools (interpolation) and a construction of a finite model, employed in [13] in the proof of Strong Finite Mode...

We prove that (1) for any complete lattice $L$, the set $\mathcal {D}(L)$ of all non-empty saturated compact subsets Scott space $L$ is a Heyting algebra (with reverse inclusion order); and (2) if latti

In this paper, we will show how one is able to construct a lattice on the completion of an algebra and to obtain an isomorphism to its Caratheodory Extension. In addition, it will be shown that the lattice form a σ-algebra and a complete Heyting algebra of countable type.

In [4, Definition 8.1], some important subvarieties of the variety SH of semi-Heyting algebras are defined. The purpose of this paper is to introduce and investigate the subvariety ISSH of SH, characterized by the identity (0  1)  (0  1)  1. We prove that ISSH contains all the subvarieties introduced by Sankappanavar and it is in fact the least subvariety of SH with this property. We als...

We show that the variety generated by the three-element Heyting algebra admits a meet dense, regular completion even though it is not closed under MacNeille completions.