Radical classes of complete lattice ordered groups
Radical classes of generalized Boolean algebras
Realization of Boolean functions by repetition-free formulas in a particular base.
Recursive prime models for Boolean algebras
Refinement Monoids, Vaught Monoids, and Boolean Algebras.
Reflexive algebras and sigma algebras.
Regulated semilattices and locally compact spaces
Relaciones entre propiedades de supremo y propiedades de interpolación en álgebras de Boole.
Relative Pseudo-Complements, Join-Extensions, and Meet-Retractions.
Remarks on cellularity in products
Remarks on measurable Boolean algebras and sequential cardinals
The paper offers a generalization of Kalton-Roberts' theorem on uniformly exhaustive Maharam's submeasures to the case of arbitrary sequentially continuous functionals. Applying the result one can reduce the problem of measurability of sequential cardinals to the question whether sequentially continuous functionals are uniformly exhaustive.
Remarks on powers of lattices
Remarks on products of σ-ideals
Remarks on the Stone Spaces of the Integers and the Reals without AC
In ZF, i.e., the Zermelo-Fraenkel set theory minus the Axiom of Choice AC, we investigate the relationship between the Tychonoff product , where 2 is 2 = 0,1 with the discrete topology, and the Stone space S(X) of the Boolean algebra of all subsets of X, where X = ω,ℝ. We also study the possible placement of well-known topological statements which concern the cited spaces in the hierarchy of weak choice principles.
Representation and duality for Hilbert algebras
In this paper we introduce a special kind of ordered topological spaces, called Hilbert spaces. We prove that the category of Hilbert algebras with semi-homomorphisms is dually equivalent to the category of Hilbert spaces with certain relations. We restrict this result to give a duality for the category of Hilbert algebras with homomorphisms. We apply these results to prove that the lattice of the deductive systems of a Hilbert algebra and the lattice of open subsets of its dual Hilbert space, are...
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,...
Representation of certain classes of distributive lattices by sections of sheaves.
Representation of Hilbert algebras and implicative semilattices
In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.
Representation theorem for finite quasi-boolean algebras
Representation Theorem for Minimal -Algebras