Computability of Distributive Lattices
- 作者: Bazhenov N.1, Frolov A.2, Kalimullin I.2, Melnikov A.3
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隶属关系:
- Sobolev Institute of Mathematics
- Kazan (Volga Region) Federal University
- Massey University
- 期: 卷 58, 编号 6 (2017)
- 页面: 959-970
- 栏目: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171546
- DOI: https://doi.org/10.1134/S0037446617060052
- ID: 171546
如何引用文章
详细
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.
作者简介
N. Bazhenov
Sobolev Institute of Mathematics
编辑信件的主要联系方式.
Email: bazhenov@math.nsc.ru
俄罗斯联邦, Novosibirsk
A. Frolov
Kazan (Volga Region) Federal University
Email: bazhenov@math.nsc.ru
俄罗斯联邦, Kazan
I. Kalimullin
Kazan (Volga Region) Federal University
Email: bazhenov@math.nsc.ru
俄罗斯联邦, Kazan
A. Melnikov
Massey University
Email: bazhenov@math.nsc.ru
新西兰, Massey