Pointwise periodic groups
Polarity compatible with a closure system
Polyabelian loops and Boolean completeness
We consider the question of which loops are capable of expressing arbitrary Boolean functions through expressions of constants and variables. We call this property Boolean completeness. It is a generalization of functional completeness, and is intimately connected to the computational complexity of various questions about expressions, circuits, and equations defined over the loop. We say that a loop is polyabelian if it is an iterated affine quasidirect product of Abelian groups; polyabelianness...
Prime ideal theorem for double Boolean algebras
Double Boolean algebras are algebras (D,⊓,⊔,⊲,⊳,⊥,⊤) of type (2,2,1,1,0,0). They have been introduced to capture the equational theory of the algebra of protoconcepts. A filter (resp. an ideal) of a double Boolean algebra D is an upper set F (resp. down set I) closed under ⊓ (resp. ⊔). A filter F is called primary if F ≠ ∅ and for all x ∈ D we have x ∈ F or . In this note we prove that if F is a filter and I an ideal such that F ∩ I = ∅ then there is a primary filter G containing F such that G...
Pseudo-galois Extensions of Boolean Algebras
Quasi locally connected toposes.
Quasi-modal algebras
In this paper we introduce the class of Boolean algebras with an operator between the algebra and the set of ideals of the algebra. This is a generalization of the Boolean algebras with operators. We prove that there exists a duality between these algebras and the Boolean spaces with a certain relation. We also give some applications of this duality.
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