Computability of Distributive Lattices
- Authors: Bazhenov N.A.1, Frolov A.N.2, Kalimullin I.S.2, Melnikov A.G.3
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Affiliations:
- Sobolev Institute of Mathematics
- Kazan (Volga Region) Federal University
- Massey University
- Issue: Vol 58, No 6 (2017)
- Pages: 959-970
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171546
- DOI: https://doi.org/10.1134/S0037446617060052
- ID: 171546
Cite item
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.
About the authors
N. A. Bazhenov
Sobolev Institute of Mathematics
Author for correspondence.
Email: bazhenov@math.nsc.ru
Russian Federation, Novosibirsk
A. N. Frolov
Kazan (Volga Region) Federal University
Email: bazhenov@math.nsc.ru
Russian Federation, Kazan
I. Sh. Kalimullin
Kazan (Volga Region) Federal University
Email: bazhenov@math.nsc.ru
Russian Federation, Kazan
A. G. Melnikov
Massey University
Email: bazhenov@math.nsc.ru
New Zealand, Massey