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Free Finitely Generated Linear Hilbert Algebras with Supremum
Sławomir Przybyło and Katarzyna Słomczyńska

The variety of Hilbert algebras with supremum form the algebraic counterpart of the implicative-join fragment of Intuitionistic Propositional Logic. We show how the elements of a finite algebra from this variety can be represented as antichains in a poset. This result allows us to construct the finitely generated free algebras in its subvariety consisting of linear Hilbert algebras with supremum and to get some bounds and asymptotics for the free spectrum of linear Hilbert algebras with supremum of height 3.

Keywords: Hilbert algebras with supremum, Fregean varieties, Gödel logic, free algebras, free spectra

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