INVESTIGADORES
CASTIGLIONI JosÉ Luis
artículos
Título:
On the variety of Heyting algebras with successor generated by all finite chains,
Autor/es:
J.L. CASTIGLIONI; H.J. SAN MART¨ªN
Revista:
Reports on Mathematical Logic
Editorial:
Jagiellonian University Press
Referencias:
Año: 2010 p. 225 - 248
ISSN:
0137-2904
Resumen:
There is a categorical duality between Heyting algebras with successor and certain Priestley spaces. Let X be the Heyting space associated by this duality to the Heyting algebra with successor H. If there is an ordinal k and a filtration on X such that X is the union over all ordinals z, smaller or equal to k, of X_z, the height of X is the minimun ordinal w ¡Ü k such that the complement of X_w is the void set. In this case, we also say that H has height w. This filtration allows us to write the space X as a disjoint union of antichains. We may think that these antichains define levels on this space. We study the way of characterize subalgebras and homomorphic images in finite Heyting algebras with successor by means of their Priestley spaces. We also depict the spaces associated to the free algebras in various subcategories of SLH.X be the Heyting space associated by this duality to the Heyting algebra with successor H. If there is an ordinal k and a filtration on X such that X is the union over all ordinals z, smaller or equal to k, of X_z, the height of X is the minimun ordinal w ¡Ü k such that the complement of X_w is the void set. In this case, we also say that H has height w. This filtration allows us to write the space X as a disjoint union of antichains. We may think that these antichains define levels on this space. We study the way of characterize subalgebras and homomorphic images in finite Heyting algebras with successor by means of their Priestley spaces. We also depict the spaces associated to the free algebras in various subcategories of SLH.