2006/01/31 by Friedrich Wehrung · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Rough Sets and Fuzzy Logic #math.RA #msc:06A12. #msc:06B10 #msc:06B15 #msc:08A30 #msc:08B10 #msc:16E50 #msc:19A49 #semigroups and automata theory
paper · pdf · doi:10.1016/j.aim.2007.05.016
published as Advances in Mathematics 216, 2 (2007) 610--625 · Version 1 presents a longer and slightly more general proof, based on so-called "uniform refinement properties". Version 2 presents a shorter proof. Versions 3 an 4 add a few minor improvements. Version 5 fixes a minor oversight in the proof of Theorem 7.1
openalex publication_date 2007/06/03 · arxiv created 2007/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
We construct a distributive algebraic lattice D that is not isomorphic to the congruence lattice of any lattice. This solves a long-standing open problem, traditionally attributed to R. P. Dilworth, from the forties. The lattice D has compact top element and aleph omega+1 compact elements. Our results extend to all algebras possessing a polynomially definable structure of a join-semilattice with a largest element.