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Vestnik Tomskogo Gosudarstvennogo Universiteta. Matematika i Mekhanika, 2018, Number 53, Pages 5–15
DOI: https://doi.org/10.17223/19988621/53/1
(Mi vtgu645)
 

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On symmetric cuts of a real-closed field

N. Yu. Galanova

Tomsk State University, Tomsk, Russian Federation
Full-text PDF (463 kB) Citations (1)
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Abstract: The paper investigates properties of a subfield of the field of bounded formal power series $\mathbf{R}[[G,\beta^+]]$, $|G|=cf(G)=\beta^+>\beta>\aleph_0$. We construct (under GCH) a real closed field $H$, $\mathbf{R}[[G,\beta]]\subset H\subset\mathbf{R}[[G,\beta^+]]$ which has symmetric cuts of cofinality $\beta^+$. We show that $H$ and $\overline{H(x_{\beta^+})}$ are truncation closed. We use G. Pestov's and S. Shelah's classifications of cuts (a symmetric cut and a non-algebraic cut).
Keywords: real closed field, truncation closed field, field of bounded formal power series, symmetric cut, cofinality of a cut.
Received: 28.01.2018
Bibliographic databases:
Document Type: Article
UDC: 512.623.23
MSC: 12F20, 12J15
Language: Russian
Citation: N. Yu. Galanova, “On symmetric cuts of a real-closed field”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2018, no. 53, 5–15
Citation in format AMSBIB
\Bibitem{Gal18}
\by N.~Yu.~Galanova
\paper On symmetric cuts of a real-closed field
\jour Vestn. Tomsk. Gos. Univ. Mat. Mekh.
\yr 2018
\issue 53
\pages 5--15
\mathnet{http://mi.mathnet.ru/vtgu645}
\crossref{https://doi.org/10.17223/19988621/53/1}
\elib{https://elibrary.ru/item.asp?id=35122601}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Вестник Томского государственного университета. Математика и механика
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    Full-text PDF :73
    References:23
     
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