On measure for projectors
An example of a finite set of projectors in is exhibited for which no 0-1 measure exists.
On a certain mapping on the set with orthogonality
On a characterization of probability measures on Boolean algebras and some orthomodular lattices
On A Class Of Sentential Functions
On a class of sentential functions.
On a Foundation for Mathematics- a View of Mathematics I
On a period of elements of pseudo-BCI-algebras
The notions of a period of an element of a pseudo-BCI-algebra and a periodic pseudo-BCI-algebra are defined. Some of their properties and characterizations are given.
On a periodic part of pseudo-BCI-algebras
In the paper the connections between the set of some maximal elements of a pseudo-BCI-algebra and deductive systems are established. Using these facts, a periodic part of a pseudo-BCI-algebra is studied.
On a representation theorem of De Morgan algebras by fuzzy sets.
Once the concept of De Morgan algebra of fuzzy sets on a universe X can be defined, we give a necessary and sufficient condition for a De Morgan algebra to be isomorphic to (represented by) a De Morgan algebra of fuzzy sets.
On a sum of observables in a logic
On a summability of observables in generalized measurable spaces
On algebras of relations
On annihilators in BL-algebras
In the paper, we introduce the notion of annihilators in BL-algebras and investigate some related properties of them. We get that the ideal lattice (I(L), ⊆) is pseudo-complemented, and for any ideal I, its pseudo-complement is the annihilator I⊥ of I. Also, we define the An (L) to be the set of all annihilators of L, then we have that (An(L); ⋂,∧An(L),⊥,0, L) is a Boolean algebra. In addition, we introduce the annihilators of a nonempty subset X of L with respect to an ideal I and study some properties...
On annihilators of BCK-algebras
On archimedean -algebras
On automorphism groups of boolean algebras
On axiom systems of pseudo-BCK algebras.
On BE-semigroups.
On Boolean modus ponens.
An abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].
On BPI Restricted to Boolean Algebras of Size Continuum
(i) The statement P(ω) = “every partition of ℝ has size ≤ |ℝ|” is equivalent to the proposition R(ω) = “for every subspace Y of the Tychonoff product the restriction |Y = Y ∩ B: B ∈ of the standard clopen base of to Y has size ≤ |(ω)|”. (ii) In ZF, P(ω) does not imply “every partition of (ω) has a choice set”. (iii) Under P(ω) the following two statements are equivalent: (a) For every Boolean algebra of size ≤ |ℝ| every filter can be extended to an ultrafilter. (b) Every Boolean algebra of...