Geodesic
Relatively complete ordered fields without integer parts
Mojtaba Moniri 1   ; Jafar S. Eivazloo 1
1 Institute for Studies in Theoretical Physics and Mathematics (IPM) Tehran, Iran
Fundamenta Mathematicae, Tome 179 (2003) no. 1, pp. 17-25 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We prove a convenient equivalent criterion for monotone completeness of ordered fields of generalized power series $[[F^G]]$ with exponents in a totally ordered Abelian group $G$ and coefficients in an ordered field $F$. This enables us to provide examples of such fields (monotone complete or otherwise) with or without integer parts, i.e. discrete subrings approximating each element within 1. We include a new and more straightforward proof that $[[F^G]]$ is always Scott complete. In contrast, the Puiseux series field with coefficients in $F$ always has proper dense field extensions.
DOI : 10.4064/fm179-1-2
Keywords: prove convenient equivalent criterion monotone completeness ordered fields generalized power series exponents totally ordered abelian group coefficients ordered field enables provide examples fields monotone complete otherwise without integer parts discrete subrings approximating each element within include straightforward proof always scott complete contrast puiseux series field coefficients always has proper dense field extensions

Mojtaba Moniri  1   ; Jafar S. Eivazloo  1

1 Institute for Studies in Theoretical Physics and Mathematics (IPM) Tehran, Iran 
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Mojtaba Moniri; Jafar S. Eivazloo. Relatively complete ordered fields
 without integer parts. Fundamenta Mathematicae, Tome 179 (2003) no. 1, pp. 17-25. doi: 10.4064/fm179-1-2

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