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An Investigation of the Fields of Bounded Formal Power Series by Means of Theory of Cuts

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Abstract

We consider a class K of real closed fields F, |F|=|G|=ℵ1, where G is a group of Archimedean classes of F, and cofinality of each symmetric gap of F is ℵ1. We will show that this class is exactly a class of all bounded formal power series R〚G,ℵ1〛, where G is a divisible Abelian group, card(G)=ℵ1, under CH. A nonstandard real line *R, which is η1-set belongs to this class; we will also consider a construction R〚G(L,P),ℵ1〛 of fields from this class, where L is a totally ordered set, P is a totally ordered field, G(L,P) is a group of finite words. It will be describes symmetric gaps of such two fields in K, which are not η1-set.

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, Tomsk State University, 36 Lenin Prosp., 634050, Tomsk, Russia

    N. Y. Galanova

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  1. N. Y. Galanova
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Mathematics Subject Classifications (2000)

03E04, 12J15, 12J25.

The work was supported by grant of Ministry of Education PD02-1.1-386.

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Galanova, N.Y. An Investigation of the Fields of Bounded Formal Power Series by Means of Theory of Cuts. Acta Appl Math 85, 121–126 (2005). https://doi.org/10.1007/s10440-004-5593-5

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