TY - GEN
T1 - Computable isomorphisms of distributive lattices
AU - Bazhenov, Nikolay
AU - Mustafa, Manat
AU - Yamaleev, Mars
N1 - Funding Information:
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.
Funding Information:
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. 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.
Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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 (formula presented) isomorphism for computable distributive lattices is (formula presented) complete. We obtain similar results for Heyting algebras, undirected graphs, and uniformly discrete metric spaces.
AB - 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 (formula presented) isomorphism for computable distributive lattices is (formula presented) complete. We obtain similar results for Heyting algebras, undirected graphs, and uniformly discrete metric spaces.
KW - Computable categoricity
KW - Computable metric space
KW - Computable reducibility
KW - Distributive lattice
KW - Equivalence relation
KW - Heyting algebra
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U2 - 10.1007/978-3-030-14812-6_3
DO - 10.1007/978-3-030-14812-6_3
M3 - Conference contribution
AN - SCOPUS:85064865052
SN - 9783030148119
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 28
EP - 41
BT - Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings
A2 - Gopal, T. V.
A2 - Watada, Junzo
PB - Springer Verlag
T2 - 15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019
Y2 - 13 April 2019 through 16 April 2019
ER -