Σ-Preorderings in \( \mathbb{H}\mathbbm{F} \)(ℝ)
- 作者: Morozov A.S.1,2
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隶属关系:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- 期: 卷 58, 编号 5 (2019)
- 页面: 405-416
- 栏目: Article
- URL: https://journals.rcsi.science/0002-5232/article/view/234155
- DOI: https://doi.org/10.1007/s10469-019-09560-0
- ID: 234155
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详细
It is proved that the ordinal ω1cannot be embedded into a preordering Σ-definable with parameters in the hereditarily finite superstructure over the real numbers. As a corollary, we obtain the descriptions of ordinals Σ-presentable over\( \mathbb{H}\mathbbm{F} \)(ℝ) and of Gödel constructive sets of the form Lα. It is also shown that there are no Σ-presentations of structures of T-, m-, 1- and tt-degrees.
作者简介
A. Morozov
Sobolev Institute of Mathematics; Novosibirsk State University
编辑信件的主要联系方式.
Email: morozov@math.nsc.ru
俄罗斯联邦, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 1, Novosibirsk, 630090
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