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Σ-Preorderings in ℍF (ℝ) Научная публикация

Журнал

Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302

Вых. Данные

Год: 2019, Том: 58, Номер: 5, Страницы: 405-416 Страниц : 12 DOI: 10.1007/s10469-019-09560-0

Ключевые слова

Hereditarily finite superstructure; Ordinal; Real numbers; Σ-definable preordering

Авторы

Morozov A.S. ^1,2

Организации

1	Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russian Federation

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 overℍF(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. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Morozov A.S.
Σ-Preorderings in ℍF (ℝ)
Algebra and Logic. 2019. V.58. N5. P.405-416. DOI: 10.1007/s10469-019-09560-0 WOS Scopus OpenAlex

Морозов А.С.
О $\Sigma$-предпорядках в ${\mathbb{HF}(\mathbb{R})}$
Алгебра и логика. 2019. Т.58. №5. С.609–626.

Web of science:	WOS:000500852800001
Scopus:	2-s2.0-85076336469
OpenAlex:	W2992594106

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