A quasiorder (relation), also known as a preorder, is a reflexive and transitive relation. The quasiorders on a set A form a complete lattice with respect to set inclusion. Assume that A is a set such that there is no inaccessible cardinal less than or equal to |A|; note that in Kuratowski's model of ZFC, all sets A satisfy this assumption. Generalizing the 1996 result of Ivan Chajda and Gábor Czéedli, also Tamás Dolgos' recent achievement, we prove that in this case the lattice of quasiorders on A is five-generated, as a complete lattice.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1248,
author = {J\'ulia Kulin},
title = {Quasiorder lattices are five-generated},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {36},
year = {2016},
pages = {59-70},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1248}
}
Júlia Kulin. Quasiorder lattices are five-generated. Discussiones Mathematicae - General Algebra and Applications, Tome 36 (2016) pp. 59-70. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1248/
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