Computable Isomorphisms of Distributive Lattices

Nikolay Bazhenov, Manat Mustafa, Mars Yamaleev

Research output: Chapter in Book/Report/Conference proceedingChapter


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 α , the relation of Δ0α isomorphism for computable distributive lattices is Σ0α+2 complete. We obtain similar results for Heyting algebras, undirected graphs, and uniformly discrete metric spaces.
Original languageEnglish
Title of host publicationTheory and Applications of Models of Computation
Subtitle of host publication15th Annual Conference, TAMC 2019, Kitakyushu, Japan, April 13–16, 2019, Proceedings
EditorsT V Gopal, Junzo Watada
PublisherSpringer International Publishing
Number of pages14
ISBN (Electronic)978-3-030-14812-6
ISBN (Print)978-3-030-14811-9
Publication statusPublished - Mar 6 2019

Publication series

NameLecture Notes in Computer Science, vol 11436. Springer, Cham


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