INVESTIGADORES
CASTIGLIONI JosÉ Luis
artículos
Título:
Errata on "On the variety of Heyting algebras with successor generated by all finite chains"
Autor/es:
J.L. CASTIGLIONI; H.J. SAN MARTÍN
Revista:
Reports on Mathematical Logic
Editorial:
Jagiellonian University Press
Referencias:
Año: 2013 vol. 48 p. 115 - 118
ISSN:
0137-2904
Resumen:
In our original article we have claimed that finite Heyting algebras with successor only generate a proper subvariety of that of all Heyting algebras with successor, and that in particular all finite chains generate a proper subvariety of the latter. As Xavier Caicedo made us notice, this claim is not true. He proved, using techniques of Kripke models, that the intuitionistic calculus with S has finite model property and from this result he concluded that the variety of Heyting algebras with successor is generated by its finite members. This fact particularly affects Section 3.2 of our article. Concretely, that stated in Remark 3.3. is not true as stated. It remains valid only if  we consider a finite ordinal.  In particular, the class of S-Heyting algebras of height omega is not a variety and the variety generated by all finite chains is exactly the variety of linear S-Heyting algebras