Lattices embeddable in three-generated lattices
Rings and Algebras
2015-12-15 v1
Abstract
We prove that every finite lattice L can be embedded in a three-generated finite lattice K. We also prove that every algebraic lattice with accessible cardinality is a complete sublattice of an appropriate algebraic lattice K such that K is completely generated by three elements. Note that ZFC has a model in which all cardinal numbers are accessible. Our results strengthen P. Crawley and R. A. Dean's 1959 results by adding finiteness, algebraicity, and completeness.
Cite
@article{arxiv.1512.03971,
title = {Lattices embeddable in three-generated lattices},
author = {Gábor Czédli},
journal= {arXiv preprint arXiv:1512.03971},
year = {2015}
}
Comments
11 pages, 3 figures