Iterated products of ideals of Borel sets
Limits of families of measure algebras
Local properties of complete Boolean products
-Polaren in halbgeordneten Mengen
Nonaccessible filters in measure algebras and functionals on
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 CCC boolean algebras and partial orders
We partially strengthen a result of Shelah from [Sh] by proving that if and is a CCC partial order with e.g. (the successor of ) and then is -linked.
On maximal submonoids of BX.
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 .
On the injectivity of Boolean algebras
The functor taking global elements of Boolean algebras in the topos of sheaves on a complete Boolean algebra is shown to preserve and reflect injectivity as well as completeness. This is then used to derive a result of Bell on the Boolean Ultrafilter Theorem in -valued set theory and to prove that (i) the category of complete Boolean algebras and complete homomorphisms has no non-trivial injectives, and (ii) the category of frames has no absolute retracts.
On the reconstruction of Boolean algebras from their automorphism groups.
Orthogonal and prereflective subcategories
Outer measure on boolean algebras
Partitions of -branching trees and the reaping number of Boolean algebras
The reaping number of a Boolean algebra is defined as the minimum size of a subset such that for each -partition of unity, some member of meets less than elements of . We show that for each , as conjectured by Dow, Steprāns and Watson. The proof relies on a partition theorem for finite trees; namely that every -branching tree whose maximal nodes are coloured with colours contains an -branching subtree using at most colours if and only if .
Relaciones entre propiedades de supremo y propiedades de interpolación en álgebras de Boole.
Remarks on cellularity in products
Remarks on powers of lattices
Remarks on products of σ-ideals
Representation of a Boolean algebra by its triangular norms.
Given a complete and atomic Boolean algebra B, there exists a family taugamma of triangular norms on B such that, under the partial ordering of triangular norms, taugamma is a Boolean algebra isomorphic to B, where gamma is the set of all atoms in B. In other words, as we have shown in this note, every complete and atomic Boolean algebra can be represented by its own triangular norms. What we have not shown in this paper is our belief that taugamma is not unique for B and that, for such a representation,...
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.