Cubic algebras and Implication Algebras

Abstract

We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra and the connection between these two operations. Finally we use the ideas of the collapse to obtain a Stone-type representation theorem for a large class of cubic algebras.

24 pages

References in corpus (2)

• A Universal Axiomatization of Metropolis-Rota Implication Algebras
• The Algebra of Filters of a Cubic Algebra