Canonical Extensions of Stone and Double Stone Algebras: the Natural Way
نویسندگان
چکیده
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.
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