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ArticleOriginal scientific text

Title

Quasiorder lattices are five-generated

Authors 1

Affiliations

  1. University of Szeged, Bolyai Institute, Szeged, Aradi vértanúk tere 1, Hungary 6720

Abstract

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.

Keywords

ENG
quasiorder lattice, preorder lattice, accessible cardinal

Bibliography

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Discussiones Mathematicae - General Algebra and Applications
2016/36/1
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Pages:
59-70
Main language of publication
English
Received
2015-10-29
Accepted
2015-11-05
Published
2016

DOI: 10.7151/dmgaa.1248

Exact and natural sciences