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arXiv · 1307.8184

Free algebras in varieties of Hilbert algebras with supremum generated by finite chains

Aldo V. Figallo·Elda Pick·Susana Saad·Martin Figallo
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Abstract

Hilbert algebras with supremum, i.e., Hilbert algebras where the associated order is a join-semilattice were first considered by A.V. Figallo, G. Ramon and S. Saad in [11], and independently by S. Celani and D. Montangie in [7]. On the other hand, L. Monteiro introduced the notion of n-valued Hilbert algebras (see [12]). In this work, we investigate the class of n-valued Hilbert algebras with supremum, denoted Hn, i.e., n-valued Hilbert algebras where the associated order is a join-semilattice. The varieties Hn are generated by finite chains. The free Hn-algebra Freen+1(r) with r generators is studied. In particular, we determine an upper bound to the cardinal of the finitely generated free algebra Freen+1(r).

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Aldo V. Figallo, Elda Pick, Susana Saad, Martin Figallo. 2013-07-31. Free algebras in varieties of Hilbert algebras with supremum generated by finite chains. https://arxiv.org/abs/1307.8184

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