Σ-Preorderings in ℍF (ℝ) Full article
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Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302 |
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| Output data | Year: 2019, Volume: 58, Number: 5, Pages: 405-416 Pages count : 12 DOI: 10.1007/s10469-019-09560-0 | ||||
| Tags | Hereditarily finite superstructure; Ordinal; Real numbers; Σ-definable preordering | ||||
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Abstract:
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.
Cite:
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
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
Original:
Морозов А.С.
О $\Sigma$-предпорядках в ${\mathbb{HF}(\mathbb{R})}$
Алгебра и логика. 2019. Т.58. №5. С.609–626.
О $\Sigma$-предпорядках в ${\mathbb{HF}(\mathbb{R})}$
Алгебра и логика. 2019. Т.58. №5. С.609–626.
Identifiers:
| Web of science: | WOS:000500852800001 |
| Scopus: | 2-s2.0-85076336469 |
| OpenAlex: | W2992594106 |
Citing:
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