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Hilbert algebras as implicative partial semilattices

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The infimum of elements a and b of a Hilbert algebra are said to be the compatible meet of a and b, if the elements a and b are compatible in a certain strict sense. The subject of the paper will be Hilbert algebras equipped with the compatible meet operation, which normally is partial. A partial lower semilattice is shown to be a reduct of such an expanded Hilbert algebra i ?both algebras have the same ?lters.An expanded Hilbert algebra is actually an implicative partial semilattice (i.e., a relative subalgebra of an implicative semilattice),and conversely.The implication in an implicative partial semilattice is characterised in terms of ?lters of the underlying partial semilattice.
Wydawca
Czasopismo
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Tom
5
Numer
2
Strony
264-279
Opis fizyczny
Daty
wydano
2007-06-01
online
2007-06-01
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-007-0008-2
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