Sequential convergences on generalized Boolean algebras

Sequential Convergences on Generalized Boolean Algebras

In this paper we investigate convergence structures on a generalized Boolean algebra and their relations to convergence structures on abelian lattice ordered groups.

Generalized Join-hemimorphisms on Boolean Algebras

We introduce the notions of generalized join-hemimorphism and generalized Boolean relation as an extension of the notions of join-hemimorphism and Boolean relation, respectively. We prove a duality between these two notions.Wewill also define a generalization of the notion of Boolean algebra with operators by considering a finite family of Boolean algebras endowed with a generalized join-hemimo...

Wreath Product Action on Generalized Boolean Algebras

Let G be a finite group acting on the finite set X such that the corresponding (complex) permutation representation is multiplicity free. There is a natural rank and order preserving action of the wreath product G ∼ Sn on the generalized Boolean algebra BX(n). We explicitly block diagonalize the commutant of this action.

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.

Continuum Cardinals Generalized to Boolean Algebras