Clones above the unary clone

2011/08/09 by Martin Goldstern, Goldstern, Martin, Gábor Sági +3
Computer Science · Mathematics · #05C25 #05C65 #08A40 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA) #math.LO #math.RA #msc:05C25 #msc:05C65 #msc:08A40

paper · pdf · doi:10.48550/arxiv.1108.2061

published as Algebra Universalis 69 No. 4 (2013) 387--399 · (infinitesimal changes to version 1)

openalex publication_date 2011/08/09 · arxiv created 2011/08/14 · arxiv updated 2011/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let c be the cardinality of the continuum. We give a family of pairwise incomparable clones (on a countable base set) 2^c members, all with the same unary fragment, namely the set of all unary operations. We also give, for each n, a family of 2^c clones all with the same n-ary fragment, and all containing the set of all unary operations.

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