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Different similarities

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Abstract

We establish the hierarchy among twelve equivalence relations (similarities) on the class of relational structures: the equality, the isomorphism, the equimorphism, the full relation, four similarities of structures induced by similarities of their self-embedding monoids and intersections of these equivalence relations. In particular, fixing a language L and a cardinal κ, we consider the interplay between the restrictions of these similarities to the class Mod L (κ) of all L-structures of size κ. It turns out that, concerning the number of different similarities and the shape of the corresponding Hasse diagram, the class of all structures naturally splits into three parts: finite structures, infinite structures of unary languages, and infinite structures of non-unary languages (where all these similarities are different).

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, Novi Sad, 21000, Serbia

    Miloš S. Kurilić

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  1. Miloš S. Kurilić
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Correspondence to Miloš S. Kurilić.

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Kurilić, M.S. Different similarities. Arch. Math. Logic 54, 839–859 (2015). https://doi.org/10.1007/s00153-015-0443-x

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  • DOI: https://doi.org/10.1007/s00153-015-0443-x

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