The aim of the present paper is to define the localisation of MValgebra of an MV-algebra A with respect to a topology F on A. In the last part of the paper it is proved that the maximal MV-algebra of quotients (defined in [6]) and the MV-algebra of fractions relative to an ∧−closed system (defined in [5]) are MV algebra of localisation. The concept of multiplier for distributive lattices was de...

We develop duality between nuclei on Heyting algebras and certain binary relations on Heyting spaces. We show that these binary relations are in 1–1 correspondence with subframes of Heyting spaces. We introduce the notions of nuclear and dense nuclear varieties of Heyting algebras, and prove that a variety of Heyting algebras is nuclear iff it is a subframe variety, and that it is dense nuclear...

Weak Heyting algebras are a natural generalization of Heyting algebras (see [2], [5]). In this work we study certain subvarieties of the variety of weak Heyting algebras in order to extend some known results about compatible functions in Heyting algebras.

The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of algebraic logic to the study of persistence based on a new operation on the ordered structure of the input diagram of vector spaces and linear maps given by a filtra...

Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of L−ordered fuzzifying convergence spaces, in which the category of L−fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called th...

We describe an algebraic way to code the causal information of a discrete spacetime. The causal set C is transformed to a description in terms of the causal pasts of the events in C. This is done by an evolving set, a functor which to each event of C assigns its causal past. Evolving sets obey a Heyting algebra which is characterised by a non-standard notion of complement. Conclusions about the...

In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite...

Allen, A. & Snary, D. (1972) Gut 13, 666-672 Florey, H. W. (1962) Gastroenterology 43, 326-329 Jencks, W. P. (1969) Catalysis in Chemistry and Enzymology, p. 393, McGraw-Hill , London Snary, D. & Allen, A. (1971) Biochem. J . 123, 845-853 Snary, D. & Allen, A. (1972) Biochem. J . 127, 577-587 Snary, D., Allen, A. & Pain, R. H. (1971) Eur. J . Biochem. 24, 183-189 Snary, D., Allen, A. & Pain, R....

A commutative residuated lattice is said to be subidempotent if the lower bounds of its neutral element e are idempotent (in which case they naturally constitute a Brouwerian algebra A*). It proved here that epimorphisms surjective in variety K such algebras (with or without involution), provided each finitely subdirectly irreducible B has two properties: (1) generated by e, and (2) poset prime...