Probability over Płonka sums of Boolean algebras: States, metrics and topology

Isomorphisms of Sums of Boolean Algebras

We prove that any Boolean algebra is a homomorphic image of a Boolean algebra B isomorphic to B + B + B but not to B + B. In [5], W. Hanf constructed a Boolean algebra H such that H is isomorphic to the direct product H X H x H but not to H x H. Hanfs result was generalized in [2] as follows. For any Abelian group (G, + ) there exists a collection of nonisomorphic Boolean algebras {B(g)\g G G} ...

Isomorphisms of Sums of Countable Boolean Algebras

Denote by nA the sum of n copies of a Boolean algebra A. We prove that, for any countable Boolean algebra A, nA at mA with m > n implies nA a (n + \)A. In [2], W. Hanf constructed a Boolean algebra H isomorphic to the direct product H X H X H but not to H X H. This result of Hanf was strengthened by J. Ketonen in [4]: there exists even a countable Boolean algebra with this property. In [1], P. ...

Boolean Algebras in Algebraic Topology

The appearance of the complete Heyting algebra in the realm of Algebraic Topology is the main topic of the paper.

Boolean algebras over partially ordered sets

Being the crossroads between Algebra, Topology, Logic, Set Theory and the Theory of Order; the class of Boolean algebras over partially ordered sets were look at as one of the sources, providing over time, new insights in Boolean algebras. Some constructions and their interconnections will be discussed, motivating along the way a list of open problems. Mathematics Subject Classification (MSC 20...

On possibility and probability measures in finite Boolean algebras