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(1 + 1 + 2)-Generated Equivalence Lattices

✍ Scribed by Gábor Czédli

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
239 KB
Volume
221
Category
Article
ISSN
0021-8693

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✦ Synopsis

pp. 573᎐586 have shown that Ž .

< < Equ A , the lattice of all equivalences of a finite set A with A G 7, has a four-element generating set such that exactly two of the generators are compara-Ž . ble. In other words, these lattices are 1 q 1 q 2 -generated. We extend this result for many infinite sets A; even for all sets if there are no inaccessible cardinals. Namely, we prove that if A is a set consisting of at least seven elements and there < < Ž . Ž . is no inaccessible cardinal F A , then the complete lattice Equ A is 1 q 1 q 2 -Ž . generated. This result is sharp in the sense that Equ A has neither a three-element generating set nor a four-element generating set with more than one pair of comparable generators.

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