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On the free implicative semilattice extension of a Hilbert algebra. (English) Zbl 1247.03136

The authors introduce the notions of strong Frink ideal and optimal deductive filter in a Hilbert algebra. They also study the homomorphisms and semi-homomorphisms of Hilbert algebras. Finally, they give another proof for the existence of a free implicative semilattice extension of a Hilbert algebra.

MSC:

03G25 Other algebras related to logic
06F35 BCK-algebras, BCI-algebras
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References:

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