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Σ-Preorderings in ℍF (ℝ). / Morozov, A. S.

In: Algebra and Logic, Vol. 58, No. 5, 01.11.2019, p. 405-416.

Research output: Contribution to journal › Article › peer-review

Harvard

Morozov, AS 2019, 'Σ-Preorderings in ℍF (ℝ)', Algebra and Logic, vol. 58, no. 5, pp. 405-416. https://doi.org/10.1007/s10469-019-09560-0

APA

Morozov, A. S. (2019). Σ-Preorderings in ℍF (ℝ). Algebra and Logic, 58(5), 405-416. https://doi.org/10.1007/s10469-019-09560-0

Vancouver

Morozov AS. Σ-Preorderings in ℍF (ℝ). Algebra and Logic. 2019 Nov 1;58(5):405-416. doi: 10.1007/s10469-019-09560-0

Author

Morozov, A. S. / Σ-Preorderings in ℍF (ℝ). In: Algebra and Logic. 2019 ; Vol. 58, No. 5. pp. 405-416.

BibTeX

@article{cda900e9d4df4aa69fc1eeb76046b12b,
title = "Σ-Preorderings in ℍF (ℝ)",
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 G{\"o}del 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.",
keywords = "Hereditarily finite superstructure, Ordinal, Real numbers, Σ-definable preordering, Sigma-definable preordering, DEFINABILITY, NONPRESENTABILITY",
author = "Morozov, {A. S.}",
year = "2019",
month = nov,
day = "1",
doi = "10.1007/s10469-019-09560-0",
language = "English",
volume = "58",
pages = "405--416",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "5",

}

RIS

TY - JOUR

T1 - Σ-Preorderings in ℍF (ℝ)

AU - Morozov, A. S.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - 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.

AB - 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.

KW - Hereditarily finite superstructure

KW - Ordinal

KW - Real numbers

KW - Σ-definable preordering

KW - Sigma-definable preordering

KW - DEFINABILITY

KW - NONPRESENTABILITY

UR - http://www.scopus.com/inward/record.url?scp=85076336469&partnerID=8YFLogxK

U2 - 10.1007/s10469-019-09560-0

DO - 10.1007/s10469-019-09560-0

M3 - Article

AN - SCOPUS:85076336469

VL - 58

SP - 405

EP - 416

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 5

ER -

ID: 22997247