Positive Presentations of Families Relative to e-Oracles
- 作者: Kalimullin I.1, Puzarenko V.1, Faizrahmanov M.2
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隶属关系:
- Kazan (Volga Region) Federal University
- Sobolev Institute of Mathematics
- 期: 卷 59, 编号 4 (2018)
- 页面: 648-656
- 栏目: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171958
- DOI: https://doi.org/10.1134/S0037446618040079
- ID: 171958
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详细
We introduce the notion of A-numbering which generalizes the classical notion of numbering. All main attributes of classical numberings are carried over to the objects considered here. The problem is investigated of the existence of positive and decidable computable A-numberings for the natural families of sets e-reducible to a fixed set. We prove that, for every computable A-family containing an inclusion-greatest set, there also exists a positive computable A-numbering. Furthermore, for certain families we construct a decidable (and even single-valued) computable total A-numbering when A is a low set; we also consider a relativization containing all cases of total sets (this in fact corresponds to computability with a usual oracle).
作者简介
I. Kalimullin
Kazan (Volga Region) Federal University
编辑信件的主要联系方式.
Email: Iskander.Kalimullin@kpfu.ru
俄罗斯联邦, Kazan
V. Puzarenko
Kazan (Volga Region) Federal University
Email: Iskander.Kalimullin@kpfu.ru
俄罗斯联邦, Kazan
M. Faizrahmanov
Sobolev Institute of Mathematics
Email: Iskander.Kalimullin@kpfu.ru
俄罗斯联邦, Novosibirsk
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