First, we introduce the concept of intuitionistic fuzzy group congruenceand we obtain the characterizations of intuitionistic fuzzy group congruenceson an inverse semigroup and a T^{*}-pure semigroup, respectively. Also,we study some properties of intuitionistic fuzzy group congruence. Next, weintroduce the notion of intuitionistic fuzzy semilattice congruence and we givethe characterization of...

In studying a general semigroup S, a natural thing to do is to decompose 5 (if possible) into the class sum of a set {Sa; aCl} of mutually disjoint subsemigroups Sa such that (1) each Sa belongs to some more or less restrictive type 13 of semigroup, and (2) the product SaSfi of any two of them is wholly contained in a third: SaSpClSy, for some yCI depending upon a and /3. We shall then say that...

A functional representation of the hyperspace monad, based on the semilattice structure of function space, is constructed.

In this note we characterize all subalgebras and homomorphic images of the free cyclic Heyting algebra, also known as the RiegerNishimura lattice N . Consequently, we prove that every subalgebra of N is projective, that a finite Heyting algebra is a subalgebra of N iff it is projective, and characterize projective homomorphic images of N . The atoms and co-atoms of the lattice of all subalgebra...

In this paper a simple proof of the completeness theorem of the intuitionistic predicate calculus with respect to the topological semantics is shown. From a technical point of view the proof of the completeness theorem is based on a Rasiowa-Sikirski-like theorem for the countable Heyting algebras which allows to embadd any countable Heyting algebra into a suitable topology in a such way that a ...

Given a Banach space X, denote by SPw(X) the set of equivalence classes of spreading models of X generated by normalized weakly null sequences in X. It is known that SPw(X) is a semilattice, i.e., it is a partially ordered set in which every pair of elements has a least upper bound. We show that every countable semilattice that does not contain an infinite increasing sequence is order isomorphi...

We extract the abstract core of finite homomorphism dualities using the techniques of Heyting algebras and (combinatorial) categories.

Let us consider the algebra H-B-M , where is a distributive lattice, is a H-algebra (Heyting algebra), is a B-algebra (Brouwer algebra), < A, 0, 1,∨,∧,⇒, −̇ > is HB-algebra (semi-Boolean algebra) [10], is a de Morgan algebra, < A, 0, 1,∨,∧,⇒,∼> is a symmetrical Heyting algebra [5] and, respectively is a symmetr...

Bounded residuated lattice ordered monoids (R -monoids) are a common generalization of pseudo-BL-algebras and Heyting algebras, i.e. algebras of the non-commutative basic fuzzy logic (and consequently of the basic fuzzy logic, the Łukasiewicz logic and the non-commutative Łukasiewicz logic) and the intuitionistic logic, respectively. In the paper we introduce and study classes of filters of bou...