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.
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