Algebra universalis

, 79:82 | Cite as

Endpoints of associated intervals for local clones on an infinite set

  • Boris A. RomovEmail author


For local clones defined on an infinite set, we present the relational description of endpoints of their associated intervals, which consist of local partial clones with the given total component. Using the established Galois closures on sets of relations, as well as extendability criteria for local partial clones, families of local clones on an infinite set with finitely definable (determined by a finite set of relations) endpoints of their associated intervals were provided. All maximal local clones on an infinite set that have a single element associated interval, called singular, are listed, based on Rosenberg’s Generic System (1984) of local clones and the author’s description (1992) of all maximal local partial clones.


Extendable partial clone Maximal local \((\hbox {partial})\) clone Positive primitive elimination set Associated interval Galois closure 

Mathematics Subject Classification

08A55 08A02 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.New YorkUSA

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