Flattening antichains with respect to the volume.
Frankl’s conjecture for large semimodular and planar semimodular lattices
A lattice is said to satisfy (the lattice theoretic version of) Frankl’s conjecture if there is a join-irreducible element such that at most half of the elements of satisfy . Frankl’s conjecture, also called as union-closed sets conjecture, is well-known in combinatorics, and it is equivalent to the statement that every finite lattice satisfies Frankl’s conjecture. Let denote the number of nonzero join-irreducible elements of . It is well-known that consists of at most elements....
Full embeddings into the categories of Boolean algebras
Hilbert-space-valued measures on Boolean algebras (extensions).
Inequalities for a Pair of Maps S x S ... S with S a Finite Set.
La catégorie des algèbres quantifiées
Lattice endomorphisms of
Logics of bipartite graphs and complete multipartite graphs
Luzin and anti-Luzin almost disjoint families
Under every uncountable almost disjoint family is either anti-Luzin or has an uncountable Luzin subfamily. This fails under CH. Related properties are also investigated.
Measure-determined enlargements of Boolean -algebras
Negaciones en retículos completos.
On measure for projectors
An example of a finite set of projectors in is exhibited for which no 0-1 measure exists.
On A Random Function Defined On A Pseudo Boolean Algebra
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 Carathéodory vector lattices
On extending of partial Boolean algebras to partial *-algebras
On extension properties for observables
On fields and ideals connected with notions of forcing
We investigate an algebraic notion of decidability which allows a uniform investigation of a large class of notions of forcing. Among other things, we show how to build σ-fields of sets connected with Laver and Miller notions of forcing and we show that these σ-fields are closed under the Suslin operation.
On minimal separating Boolean algebras.
On minimal spectrum of multiplication lattice modules
We study the minimal prime elements of multiplication lattice module over a -lattice . Moreover, we topologize the spectrum of minimal prime elements of and study several properties of it. The compactness of is characterized in several ways. Also, we investigate the interplay between the topological properties of and algebraic properties of .