Canonical extensions of Stone and double Stone algebras: the natural way
Miroslav Haviar, Hilary A. Priestley · Czech digital mathematics library · 2006
A construction of canonical extensions of Stone algebras is presented that uses the natural duality based on the three-element generating algebra 3 rather than the Priestley duality based on 2 that is traditionally used to build the canonical extension.The new approach has the advantage that the canonical extension so constructed inherits its algebra structure pointwise from a power of the generator, so that the extension of the fundamental operations and closure of the variety under the formation of canonical extensions occur in a transparent way.An analogous construction is outlined for two further varieties, indicating that the method has the potential to be applied in a similar manner to other classes of bounded distributive lattice expansions.