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.