Geodesic
On symmetric cuts of a real-closed field
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 53 (2018), pp. 5-15

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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. 
@article{VTGU_2018_53_a0,
     author = {N. Yu. Galanova},
     title = {On symmetric cuts of a real-closed field},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {5--15},
     publisher = {mathdoc},
     number = {53},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2018_53_a0/}
}
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N. Yu. Galanova. On symmetric cuts of a real-closed field. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 53 (2018), pp. 5-15. http://geodesic.mathdoc.fr/item/VTGU_2018_53_a0/