A Hierarchy of Algebras for Boolean Subsets.
Walter Guttmann, Bernhard Möller · OPUS (Augsburg University) · 2020
We present a collection of axiom systems for the construction of Boolean subalgebras of larger overall algebras. The subalgebras are defined as the range of a complement-like operation on a semilattice. This technique has been used, for example, with the antidomain operation, dynamic negation and Stone algebras. We present a common ground for these constructions based on a new equational axiomatisation of Boolean algebras.