Hilbert algebras as implicative partial semilattices

Jānis Cīrulis

Open Mathematics (2007)

  • Volume: 5, Issue: 2, page 264-279
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Jānis Cīrulis. "Hilbert algebras as implicative partial semilattices." Open Mathematics 5.2 (2007): 264-279. <http://eudml.org/doc/269445>.

@article{JānisCīrulis2007,
abstract = {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.},
author = {Jānis Cīrulis},
journal = {Open Mathematics},
keywords = {Compatible elements; filter; Hilbert algebra; implication; implicative semilattice; meet; partial semilattice; compatible elements; compatible meet operation},
language = {eng},
number = {2},
pages = {264-279},
title = {Hilbert algebras as implicative partial semilattices},
url = {http://eudml.org/doc/269445},
volume = {5},
year = {2007},
}

TY - JOUR
AU - Jānis Cīrulis
TI - Hilbert algebras as implicative partial semilattices
JO - Open Mathematics
PY - 2007
VL - 5
IS - 2
SP - 264
EP - 279
AB - 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.
LA - eng
KW - Compatible elements; filter; Hilbert algebra; implication; implicative semilattice; meet; partial semilattice; compatible elements; compatible meet operation
UR - http://eudml.org/doc/269445
ER -

References

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