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\({\aleph_{0}}\) -categorical structures: endomorphisms and interpretations

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Abstract

We extend the Ahlbrandt–Ziegler analysis of interpretability in \({\aleph_{0}}\)-categorical structures by showing that existential interpretation is controlled by the monoid of self–embeddings, and positive existential interpretation of structures without constant endomorphisms is controlled by the monoid of endomorphisms, in the same way as general interpretability is controlled by the automorphism group.

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Authors and Affiliations

  1. Laboratoire d’Informatique de l’École Polytechnique, 91128, Palaiseau, France

    Manuel Bodirsky

  2. Albert–Ludwigs–Universität Freiburg, Abteilung für Mathematische Logik, Eckerstraße 1, 79104, Freiburg, Germany

    Markus Junker

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  1. Manuel Bodirsky
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  2. Markus Junker
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Correspondence to Markus Junker.

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Presented by M. Valeriote.

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Bodirsky, M., Junker, M. \({\aleph_{0}}\) -categorical structures: endomorphisms and interpretations. Algebra Univers. 64, 403–417 (2010). https://doi.org/10.1007/s00012-011-0110-y

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  • DOI: https://doi.org/10.1007/s00012-011-0110-y

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