Lebesgue theory on a Boolean algebra

Ternary Boolean Algebra

Boolean Algebra Approximations

Knight and Stob proved that every low4 Boolean algebra is 0-isomorphic to a computable one. Furthermore, for n = 1, 2, 3, 4, every lown Boolean algebra is 0-isomorphic to a computable one. We show that this is not true for n = 5: there is a low5 Boolean algebra that is not 0-isomorphic to any computable Boolean algebra. It is worth remarking that, because of the machinery developed, the proof u...

A Crash Course on the Lebesgue Integral and Measure Theory

This booklet is an exposition on the Lebesgue integral. I originally started it as a set of notes consolidating what I had learned on on Lebesgue integration theory, and published them in case somebody else may find them useful. Since there are already countless books on measure theory and integration written by professional mathematicians, that teach the same things on the basic level, you may...

Free Boolean Algebra

This theory defines a type constructor representing the free Boolean algebra over a set of generators. Values of type (α)formula represent propositional formulas with uninterpreted variables from type α, ordered by implication. In addition to all the standard Boolean algebra operations, the library also provides a function for building homomorphisms to any other Boolean algebra type. 1 Free Boo...

The Lattice of Contact Relations on a Boolean Algebra

Contact relations on an algebra have been studied since the early part of the previous century, and have recently become a powerful tool in several areas of artificial intelligence, in particular, qualitative spatial reasoning and ontology building. In this paper we investigate the structure of the set of all contact relations on a Boolean algebra.