A rigid Boolean algebra that admits the elimination of Q21
Using ♢ , we construct a rigid atomless Boolean algebra that has no uncountable antichain and that admits the elimination of the Malitz quantifier .
A sandwich theorem for monotone additive functions.
A scheme for congruence semidistributivity
A diagrammatic statement is developed for the generalized semidistributive law in case of single algebras assuming that their congruences are permutable. Without permutable congruences, a diagrammatic statement is developed for the ∧-semidistributive law.
A selection property of the boolean -calculus and some of its applications
A selection theorem for Boolean correspondences.
A set-theoretical equivalent of the prime ideal theorem for Boolean algebras
A sharp bound for the reconstruction of partitions.
A short note on lattices allowing disjunctive reasoning.
This short note shows that the scheme of disjunctive reasoning, a or b, not b : a, does not hold neither in proper ortholattices nor in proper de Morgan algebras. In both cases the scheme, once translated into the inequality b' · (a+b) ≤ a, forces the structure to be a boolean algebra.
A short note on separable frames
Following the introduction of separability in frames ([2]) we investigate further properties of this notion and establish some consequences of the Urysohn metrization theorem for frames that are frame counterparts of corresponding results in spaces. In particular we also show that regular subframes of compact metrizable frames are metrizable.
A shrinking of a category of societies is a universal partly ordered class
A simple basis of ideal terms of Brouwerian semilattices
A simple geometric proof of a theorem on
A simple proof of Suzumura's extension theorem for finite domains with applications.
A simple proof of Vinogradov’s theorem on the orderability of the free product of -groups
A simplified proof of the Daniell integral extension theorem in ordered spaces
A solution of Dedekind's problem on the number of isotone Boolean functions.
A spectral construction of a treed domain that is not going-down
A strongly diagonal power of algebraic order bounded disjointness preserving operators.
A structure theorem for right invariant right holoids.
A study of independence in a set with orthogonality