Hilbert algebras as implicative partial semilattices

• Autorzy: Jānis Cīrulis
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Compatible elements; filter; Hilbert algebra; implication; implicative semilattice; meet; partial semilattice

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 2
• Strony: 264-279

Daty

wydano

2007-06-01

online

2007-06-01

Twórcy

autor

Jānis Cīrulis

• University of Latvia,

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Identyfikatory

DOI

10.2478/s11533-007-0008-2