Computable Isomorphisms of Distributive Lattices

  • Nikolay BazhenovEmail author
  • Manat Mustafa
  • Mars Yamaleev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11436)


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.


Distributive lattice Computable reducibility Equivalence relation Computable categoricity Heyting algebra Computable metric space 



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. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.Department of Mathematics, School of Science and TechnologyNazarbayev UniversityAstanaKazakhstan
  4. 4.Kazan Federal UniversityKazanRussia

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