Incomparably continuable sets of semilattices

Jaroslav Ježek; Václav Slavík

Mathematica Bohemica (2000)

  • Volume: 125, Issue: 2, page 135-137
  • ISSN: 0862-7959

Abstract

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A finite set of finite semilattices is said to be incomparably continuable if it can be extended to an infinite set of pairwise incomparable (with respect to embeddability) finite semilattices. After giving some simple examples we show that the set consisting of the four-element Boolean algebra and the four-element fork is incomparably continuable.

How to cite

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Ježek, Jaroslav, and Slavík, Václav. "Incomparably continuable sets of semilattices." Mathematica Bohemica 125.2 (2000): 135-137. <http://eudml.org/doc/248653>.

@article{Ježek2000,
abstract = {A finite set of finite semilattices is said to be incomparably continuable if it can be extended to an infinite set of pairwise incomparable (with respect to embeddability) finite semilattices. After giving some simple examples we show that the set consisting of the four-element Boolean algebra and the four-element fork is incomparably continuable.},
author = {Ježek, Jaroslav, Slavík, Václav},
journal = {Mathematica Bohemica},
keywords = {semilattice; embedding; semilattice; embedding},
language = {eng},
number = {2},
pages = {135-137},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Incomparably continuable sets of semilattices},
url = {http://eudml.org/doc/248653},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Ježek, Jaroslav
AU - Slavík, Václav
TI - Incomparably continuable sets of semilattices
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 2
SP - 135
EP - 137
AB - A finite set of finite semilattices is said to be incomparably continuable if it can be extended to an infinite set of pairwise incomparable (with respect to embeddability) finite semilattices. After giving some simple examples we show that the set consisting of the four-element Boolean algebra and the four-element fork is incomparably continuable.
LA - eng
KW - semilattice; embedding; semilattice; embedding
UR - http://eudml.org/doc/248653
ER -

References

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  1. R. McKenzie G. McNulty W. Taylor, Algebras, Lattices, Varieties, Vol. I, Wadsworth & Brooks/Cole, Monterey, CA, 1987. (1987) MR0883644

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