Geodesic
Symmetry of Sections in Fields of Formal Power Series and a Non-Standard Real Line
Algebra i logika, Tome 42 (2003) no. 1, pp. 26-36 
N. Yu. Galanova. Symmetry of Sections in Fields of Formal Power Series and a Non-Standard Real Line. Algebra i logika, Tome 42 (2003) no. 1, pp. 26-36. http://geodesic.mathdoc.fr/item/AL_2003_42_1_a1/
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     author = {N. Yu. Galanova},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $R[[G,\beta]]$ be a field of formal power series with real coefficients, whose supports are well ordered subsets of an Abelian group $G$ of cardinality strictly less than $\beta$. For $R[[G,\beta]]$, we give criteria of a section being symmetric and of a symmetric section being Dedekind. It is proved that an $\alpha^+$-saturated non-standard real line $^{*}R$ is isomorphic to some field of the form $R[[G,\alpha^+]]$. For $^{*}R$, some consequences are inferred regarding symmetric sections, and the cofinality of “banks” of the sections.

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