A Hierarchy of Algebras for Boolean Subsets

Walter Guttmann 🌐 and Bernhard Möller 🌐

January 31, 2020

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Abstract

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.
BSD License

Topics

Theories of Subset_Boolean_Algebras