2014/01/22 by Karsten Schölzel, Schölzel, Karsten
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.1401.5665
submitted to Algebra Universalis
arxiv created 2014/01/22 · openalex publication_date 2014/01/22 · arxiv updated 2014/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The following result has been shown recently in the form of a dichotomy: For every total clone C on 2 := \0,1\, the set I(C) of all partial clones on 2 whose total component is C, is either finite or of continuum cardinality. In this paper we show that the dichotomy holds, even if only strong partial clones are considered, i.e., partial clones which are closed under taking subfunctions: For every total clone C on 2, the set IStr(C) of all strong partial clones on 2 whose total component is C, is either finite or of continuum cardinality.