On a Question of J. Hashimoto
On a question of K. Leeb
On a radical class of lattice ordered groups
On A Random Function Defined On A Pseudo Boolean Algebra
On a Representation of Lattices by Congruence Relations
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 special class of left-continuous uninorms
This paper is devoted to the study of a class of left-continuous uninorms locally internal in the region and the residual implications derived from them. It is shown that such uninorm can be represented as an ordinal sum of semigroups in the sense of Clifford. Moreover, the explicit expressions for the residual implication derived from this special class of uninorms are given. A set of axioms is presented that characterizes those binary functions for which a uninorm of this special class exists...
On a sufficient condition for strong constructivizability of atomic Boolean algebras.
On a sum of observables in a logic
On A System Of All Maximal Chains (Antichains) Of A Graph
On a theorem of Baumgartner and Weese
On a theorem of Cantor-Bernstein type for algebras
Freytes proved a theorem of Cantor-Bernstein type for algbras; he applied certain sequences of central elements of bounded lattices. The aim of the present paper is to extend the mentioned result to the case when the lattices under consideration need not be bounded; instead of sequences of central elements we deal with sequences of internal direct factors of lattices.
On a Theory of Scale Types.
On a weak Freudenthal spectral theorem
Let be an Archimedean Riesz space and its Boolean algebra of all band projections, and put and , . is said to have Weak Freudenthal Property () provided that for every the lattice is order dense in the principal band . This notion is compared with strong and weak forms of Freudenthal spectral theorem in Archimedean Riesz spaces, studied by Veksler and Lavrič, respectively. is equivalent to -denseness of in for every , and every Riesz space with sufficiently many projections...
On absolute retracts and absolute convex retracts in some classes of l-groups
By dealing with absolute retracts of l-groups we use a definition analogous to that applied by Halmos for the case of Boolean algebras. The main results of the present paper concern absolute convex retracts in the class of all archimedean l-groups and in the class of all complete l-groups.
On absolute retracts of ω*
An extremally disconnected space is called an absolute retract in the class of all extremally disconnected spaces if it is a retract of any extremally disconnected compact space in which it can be embedded. The Gleason spaces over dyadic spaces have this property. The main result of this paper says that if a space X of π-weight is an absolute retract in the class of all extremally disconnected compact spaces and X is homogeneous with respect to π-weight (i.e. all non-empty open sets have the same...
On absolutely divergent series
We show that in the -stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P(ω)/fin. This complements Vojtáš’ result that under the two algebras are isomorphic [15].
On AC-lattices in which the ideal of the finite elements is standard
On adjoining units to hyper-archimedean -groups
On algebra homomorphisms in complex almost -algebras
Extensions of order bounded linear operators on an Archimedean vector lattice to its relatively uniform completion are considered and are applied to show that the multiplication in an Archimedean lattice ordered algebra can be extended, in a unique way, to its relatively uniform completion. This is applied to show, among other things, that any order bounded algebra homomorphism on a complex Archimedean almost -algebra is a lattice homomorphism.