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The Lattice of Definability. Origins, Recent Developments, and Further Directions

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Computer Science - Theory and Applications (CSR 2014)

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Abstract

The paper presents recent results and open problems on classes of definable relations (definability spaces, reducts, relational algebras) as well as sources for the research starting from the XIX century. Finiteness conditions are investigated, including quantifier alternation depth and number of arguments width. The infinite lattice of definability for integers with a successor function (a non ω-categorical structure) is described. Methods of investigation include study of automorphism groups of elementary extensions of structures under consideration, using Svenonius theorem and a generalization of it.

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Author information

Authors and Affiliations

  1. Moscow State University, Russia

    Alexei Semenov & Vladimir Uspensky

  2. Dorodnicyn Computing Center, The Russian Academy of Sciences, Russia

    Alexei Semenov & Sergey Soprunov

  3. Moscow Pedagogical State University, Russia

    Alexei Semenov

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  1. Alexei Semenov
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  2. Sergey Soprunov
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  3. Vladimir Uspensky
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Editors and Affiliations

  1. Steklov Institute of Mathematics at St. Petersburg, Russian Academy of Sciences, 27 Fontanka,, 191023, St. Petersburg, Russia

    Edward A. Hirsch

  2. Higher School of Economics, National Research University, 109028, Moscow, Russia

    Sergei O. Kuznetsov

  3. CNRS and University Paris Diderot, Paris, France

    Jean-Éric Pin

  4. Moscow State University, 119992, Moscow, Russia

    Nikolay K. Vereshchagin

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Semenov, A., Soprunov, S., Uspensky, V. (2014). The Lattice of Definability. Origins, Recent Developments, and Further Directions. In: Hirsch, E.A., Kuznetsov, S.O., Pin, JÉ., Vereshchagin, N.K. (eds) Computer Science - Theory and Applications. CSR 2014. Lecture Notes in Computer Science, vol 8476. Springer, Cham. https://doi.org/10.1007/978-3-319-06686-8_3

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  • DOI: https://doi.org/10.1007/978-3-319-06686-8_3

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