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International Conference on Theory and Applications of Models of Computation

TAMC 2019: Theory and Applications of Models of Computation pp 28–41Cite as

Computable Isomorphisms of Distributive Lattices

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11436))

Abstract

A standard tool for the classifying computability-theoretic complexity of equivalence relations is provided by computable reducibility. This gives rise to a rich degree-structure which has been extensively studied in the literature. In this paper, we show that equivalence relations, which are complete for computable reducibility in various levels of the hyperarithmetical hierarchy, arise in a natural way in computable structure theory. We prove that for any computable successor ordinal \(\alpha \), the relation of \(\varDelta ^0_{\alpha }\) isomorphism for computable distributive lattices is \(\varSigma ^0_{\alpha +2}\) complete. We obtain similar results for Heyting algebras, undirected graphs, and uniformly discrete metric spaces.

The work was supported by Nazarbayev University Faculty Development Competitive Research Grants N090118FD5342. The first author was supported by Russian Science Foundation, project No. 18-11-00028. The last author was supported by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project № 1.13556.2019/13.1.

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Acknowledgments

Part of the research contained in this paper was carried out while the first and the last authors were visiting the Department of Mathematics of Nazarbayev University, Astana. The authors wish to thank Nazarbayev University for its hospitality.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., Novosibirsk, 630090, Russia

    Nikolay Bazhenov

  2. Novosibirsk State University, 2 Pirogova St., Novosibirsk, 630090, Russia

    Nikolay Bazhenov

  3. Department of Mathematics, School of Science and Technology, Nazarbayev University, 53 Qabanbaybatyr Avenue, Astana, 010000, Kazakhstan

    Manat Mustafa

  4. Kazan Federal University, 18 Kremlevskaya St., Kazan, 420008, Russia

    Mars Yamaleev

Authors
  1. Nikolay Bazhenov
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  2. Manat Mustafa
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  3. Mars Yamaleev
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Correspondence to Nikolay Bazhenov .

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Editors and Affiliations

  1. Anna University, Chennai, India

    T.V. Gopal

  2. Waseda University, Kitakyushu, Japan

    Junzo Watada

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Bazhenov, N., Mustafa, M., Yamaleev, M. (2019). Computable Isomorphisms of Distributive Lattices. In: Gopal, T., Watada, J. (eds) Theory and Applications of Models of Computation. TAMC 2019. Lecture Notes in Computer Science(), vol 11436. Springer, Cham. https://doi.org/10.1007/978-3-030-14812-6_3

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  • DOI: https://doi.org/10.1007/978-3-030-14812-6_3

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