2015/12/12 by Gábor Czédli, Czédli, Gábor
Mathematics · #06B99 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:06B99
paper · pdf · doi:10.48550/arxiv.1512.03971
11 pages, 3 figures
arxiv created 2015/12/12 · arxiv updated 2015/12/15
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.