2013/05/04 by Gábor Czédli, Gabor Czedli, Czedli, Gabor
Computer Science · Decision Sciences · Mathematics · #06B10 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic #math.RA #msc:06B10
paper · pdf · doi:10.48550/arxiv.1305.0965
17 pages, 6 figures
openalex publication_date 2013/05/04 · arxiv created 2013/05/07 · arxiv updated 2013/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a lattice L, let Princ L denote the ordered set of principal congruences of L. In a pioneering paper, G. Gratzer characterized the ordered sets Princ L of finite lattices L; here we do the same for countable lattices. He also showed that each bounded ordered set H is isomorphic to Princ L of a bounded lattice L. We prove a related statement: if an ordered set H with least element is the union of a chain of principal order ideals, then H is isomorphic to Princ L of some lattice L.