Some cardinal characteristics of ordered sets
For ordered (= partially ordered) sets we introduce certain cardinal characteristics of them (some of those are known). We show that these characteristics—with one exception—coincide.
Some chain conditions on weak incidence algebras.
Some characterizations of completeness for trellises in terms of joins of cycles
This paper gives some new characterizations of completeness for trellises by introducing the notion of a cycle-complete trellis. One of our results yields, in particular, a characterization of completeness for trellises of finite length due to K. Gladstien (see K. Gladstien: Characterization of completeness for trellises of finite length, Algebra Universalis 3 (1973), 341–344).
Some fixed point theorems of the mappings of partially ordered sets
Some Geometric Applications of Dilworth's Theorem.
Some lattices of closure systems on a finite set.
Some operations related with translation
Some properties of an ordering relation on certain classes of functors
Some properties of boolean ordered sets
Some properties of Eulerian lattices
In this paper, we prove that Eulerian lattices satisfying some weaker conditions for lattices or some weaker conditions for 0-distributive lattices become Boolean.
Some quasi-ordered classes of finite commutative semigroups.
Some remarks on certain classes of semilattices.
Some remarks on distributive semilattices
In this paper we shall give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we will present some new ones through annihilators and relative maximal filters. We shall also simplify the topological representation for distributive semilattices given in Celani S.A., Topological representation of distributive semilattices, Sci. Math. Japonicae online 8 (2003), 41–51, and show that the meet-relations are closed under composition....
Some special subsets of intervals of a locally finite locally semi-modular, local lattice.
Sortable elements for quivers with cycles.
Splitting numbers of grids.
Standard and nonstandard representability of positive uncertainty orderings
Axioms are given for positive comparative probabilities and plausibilities defined either on Boolean algebras or on arbitrary sets of events. These axioms allow to characterize binary relations representable by either standard or nonstandard measures (i. e. taking values either on the real field or on a hyperreal field). We also study relations between conditional events induced by preferences on conditional acts.
Standard completions for quasiordered sets.
Standard paths in another composition poset.
Stationary sets, trees and continuums.