Computable Isomorphisms of Distributive Lattices

Nikolay Bazhenov, Manat Mustafa, Mars Yamaleev

Research output: Chapter in Book/Report/Conference proceedingChapter

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 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
Pages28-41
Number of pages14
Volume11436
Edition1
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
PublisherSpringer

Fingerprint

Distributive Lattice
Reducibility
Equivalence relation
Isomorphism
Computable Structure
Heyting Algebra
Computability
Undirected Graph
Metric space
Hierarchy
Standards

Cite this

Bazhenov, N., Mustafa, M., & Yamaleev, M. (2019). Computable Isomorphisms of Distributive Lattices. In T. V. Gopal, & J. Watada (Eds.), Theory and Applications of Models of Computation: 15th Annual Conference, TAMC 2019, Kitakyushu, Japan, April 13–16, 2019, Proceedings (1 ed., Vol. 11436, pp. 28-41). (Lecture Notes in Computer Science, vol 11436. Springer, Cham). Springer International Publishing.

Computable Isomorphisms of Distributive Lattices. / Bazhenov, Nikolay; Mustafa, Manat; Yamaleev, Mars.

Theory and Applications of Models of Computation: 15th Annual Conference, TAMC 2019, Kitakyushu, Japan, April 13–16, 2019, Proceedings. ed. / T V Gopal; Junzo Watada. Vol. 11436 1. ed. Springer International Publishing, 2019. p. 28-41 (Lecture Notes in Computer Science, vol 11436. Springer, Cham).

Research output: Chapter in Book/Report/Conference proceedingChapter

Bazhenov, N, Mustafa, M & Yamaleev, M 2019, Computable Isomorphisms of Distributive Lattices. in TV Gopal & J Watada (eds), Theory and Applications of Models of Computation: 15th Annual Conference, TAMC 2019, Kitakyushu, Japan, April 13–16, 2019, Proceedings. 1 edn, vol. 11436, Lecture Notes in Computer Science, vol 11436. Springer, Cham, Springer International Publishing, pp. 28-41.
Bazhenov N, Mustafa M, Yamaleev M. Computable Isomorphisms of Distributive Lattices. In Gopal TV, Watada J, editors, Theory and Applications of Models of Computation: 15th Annual Conference, TAMC 2019, Kitakyushu, Japan, April 13–16, 2019, Proceedings. 1 ed. Vol. 11436. Springer International Publishing. 2019. p. 28-41. (Lecture Notes in Computer Science, vol 11436. Springer, Cham).
Bazhenov, Nikolay ; Mustafa, Manat ; Yamaleev, Mars. / Computable Isomorphisms of Distributive Lattices. Theory and Applications of Models of Computation: 15th Annual Conference, TAMC 2019, Kitakyushu, Japan, April 13–16, 2019, Proceedings. editor / T V Gopal ; Junzo Watada. Vol. 11436 1. ed. Springer International Publishing, 2019. pp. 28-41 (Lecture Notes in Computer Science, vol 11436. Springer, Cham).
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