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# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Relatively complete ordered fields without integer parts

### Tom 179 / 2003

Fundamenta Mathematicae 179 (2003), 17-25 MSC: 12J15, 13J05, 54H13. DOI: 10.4064/fm179-1-2

#### Streszczenie

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.

#### Autorzy

• Mojtaba MoniriInstitute for Studies in Theoretical
Physics and Mathematics (IPM)
Tehran, Iran
e-mail
• Jafar S. EivazlooInstitute for Studies in Theoretical
Physics and Mathematics (IPM)
Tehran, Iran
e-mail

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