José L. Castiglioni

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A b s t r a c t. Contrary to the variety of Heyting algebras, finite Heyting algebras with successor only generate a proper subvariety of that of all Heyting algebras with successor. In particular, all finite chains generate a proper subvariety, SLH ω , of the latter. There is a categorical duality between Heyting algebras with successor and certain(More)
The (dual) Dold-Kan correspondence says that there is an equivalence of categories K : Ch ≥0 → Ab ∆ between nonneg-atively graded cochain complexes and cosimplicial abelian groups, which is inverse to the normalization functor. We show that the restriction of K to DG-rings can be equipped with an associative product and that the resulting functor DGR * →(More)
In [3] we have claimed that finite Heyting algebras with successor only generate a proper subvariety of that of all Heyting algebras with successor, and 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(More)