Free skew Boolean algebras

Free skew Boolean algebras

Representing free Boolean algebras

Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with א1 generators is represented. It w...

Extensions of Free Boolean Algebras

In a series of papers [2, 3, 4, 5], B. Efimov has given sufficient conditions for a Boolean algebra to have a free subalgebra of given cardinality. For example, he has shown that if an infinite Boolean algebra A has cardinality greater than exp exp exp v, but the supremum of the cardinalities of subsets of disjoint elements in A is not greater than v, then A has a free subalgebra with (exp v) i...

Stone Duality for Skew Boolean Algebras with Intersections

We extend Stone duality between generalized Boolean algebras and Boolean spaces, which are the zero-dimensional locally-compact Hausdorff spaces, to a non-commutative setting. We first show that the category of right-handed skew Boolean algebras with intersections is dual to the category of surjective étale maps between Boolean spaces. We then extend the duality to skew Boolean algebras with in...

On Functions Defined on Free Boolean Algebras

We characterize measures on free Boolean algebras and we examine the relationships that exists between measures and binary tables in relational databases. It is shown that these measures are completely defined by their values on positive conjunctions and an algorithm that leads to the construction of measures starting from its values on positive conjunction is also given, including a formula th...