Canonical extensions of Stone and double Stone algebras: the natural way

Rok, strany: 2006, 53 - 78

A construction of canonical extensions of Stone algebras is presented that uses the natural duality based on the three-element generating algebra $\bold 3$ rather than the Priestley duality based on $\bold 2$ 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.

ISO 690:

Haviar, M., Priestley, H. 2006. Canonical extensions of Stone and double Stone algebras: the natural way. In Mathematica Slovaca, vol. 56, no.1, pp. 53-78. 0139-9918.

APA:

Haviar, M., Priestley, H. (2006). Canonical extensions of Stone and double Stone algebras: the natural way. Mathematica Slovaca, 56(1), 53-78. 0139-9918.