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Polymorphism clones of homogeneous structures: generating sets, Sierpiński rank, cofinality and the Bergman property

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Abstract

In this paper, motivated by classical results by Sierpiński, Arnold and Kolmogorov, we derive sufficient conditions for polymorphism clones of homogeneous structures to have a generating set of bounded arity. We use our findings in order to describe a class of homogeneous structures whose polymorphism clones have a finite Sierpiński rank, uncountable cofinality, and the Bergman property.

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Authors and Affiliations

  1. Radebeul, Germany

    Christian Pech

  2. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia

    Maja Pech

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  1. Christian Pech
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  2. Maja Pech
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Correspondence to Maja Pech.

Additional information

This article is part of the topical collection “The 5th Novi Sad Algebraic Conference (NSAC 2017)” edited by P. Marković, M. Maróti and A. Tepavčević

The second author was supported by the Ministry of Education and Science of the Republic of Serbia through Grant no.174018.

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Pech, C., Pech, M. Polymorphism clones of homogeneous structures: generating sets, Sierpiński rank, cofinality and the Bergman property. Algebra Univers. 79, 45 (2018). https://doi.org/10.1007/s00012-018-0527-7

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  • DOI: https://doi.org/10.1007/s00012-018-0527-7

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