Abstract
The class of (not necessarily distributive) countable lattices is HKSS-universal, and it is also known that the class of countable linear orders is not universal with respect to degree spectra neither to computable categoricity. We investigate the intermediate class of distributive lattices and construct a distributive lattice with degree spectrum {d: d ≠ 0}. It is not known whether a linear order with this property exists. We show that there is a computably categorical distributive lattice that is not relatively Δ20-categorical. It is well known that no linear order can have this property. The question of the universality of countable distributive lattices remains open.
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Original Russian Text Copyright © 2017 Bazhenov N.A., Frolov A.N, Kalimullin I.Sh., and Melnikov A.G.
N. A. Bazhenov was supported by the Russian Foundation for Basic Research (Grant 16–31–60058-mol a dk). A. N. Frolov was supported by the Russian Foundation for Basic Research (Grant 16–31–60077–mol a dk). I. Sh. Kalimullin was supported by the Russian Foundation for Basic Research (Grant 15–41–02507) and the Ministry of Education and Science of the Russian Federation (Grant 1.451.2016/1.4). A. G. Melnikov was partially supported by the Marsden Fund of New Zealand and the Massey University Early Career Research Fund.
Novosibirsk; Kazan; Massey. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 6, pp. 1236–1251, November–December, 2017
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Bazhenov, N.A., Frolov, A.N., Kalimullin, I.S. et al. Computability of Distributive Lattices. Sib Math J 58, 959–970 (2017). https://doi.org/10.1134/S0037446617060052
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DOI: https://doi.org/10.1134/S0037446617060052