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.
@article{bwmeta1.element.doi-10_2478_s11533-007-0008-2,
author = {J\=anis C\=\i rulis},
title = {Hilbert algebras as implicative partial semilattices},
journal = {Open Mathematics},
volume = {5},
year = {2007},
pages = {264-279},
zbl = {1125.03047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0008-2}
}
Jānis Cīrulis. Hilbert algebras as implicative partial semilattices. Open Mathematics, Tome 5 (2007) pp. 264-279. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0008-2/
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