2004/01/10 by Michael Pinsker, Pinsker, Michael
Computer Science · Mathematics · #08A05 #08A40 #Advanced Algebra and Logic #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA) #math.LO #math.RA #msc:08A05 #msc:08A40 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0401102
20 pages
arxiv created 2004/01/10 · openalex publication_date 2004/01/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be an infinite set of regular cardinality. We determine all clones on X which contain all almost unary functions. It turns out that independently of the size of X, these clones form a countably infinite descending chain. Moreover, all such clones are finitely generated over the unary functions. In particular, we obtain an explicit description of the only maximal clone in this part of the clone lattice. This is especially interesting if X is countably infinite, in which case it is known that such a description cannot be obtained for the second maximal clone over the unary functions.