Computability of Distributive Lattices
- Авторы: Bazhenov N.1, Frolov A.2, Kalimullin I.2, Melnikov A.3
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Учреждения:
- Sobolev Institute of Mathematics
- Kazan (Volga Region) Federal University
- Massey University
- Выпуск: Том 58, № 6 (2017)
- Страницы: 959-970
- Раздел: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171546
- DOI: https://doi.org/10.1134/S0037446617060052
- ID: 171546
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Аннотация
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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Об авторах
N. Bazhenov
Sobolev Institute of Mathematics
Автор, ответственный за переписку.
Email: bazhenov@math.nsc.ru
Россия, Novosibirsk
A. Frolov
Kazan (Volga Region) Federal University
Email: bazhenov@math.nsc.ru
Россия, Kazan
I. Kalimullin
Kazan (Volga Region) Federal University
Email: bazhenov@math.nsc.ru
Россия, Kazan
A. Melnikov
Massey University
Email: bazhenov@math.nsc.ru
Новая Зеландия, Massey