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IPM
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“School of Mathematics”

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Paper   IPM / M / 2355
School of Mathematics
  Title:   Relatively complete ordered fields without integer parts
  Author(s): 
1.  Moj. Moniri
2.  J. S. Eivazloo
  Status:   Published
  Journal: Fund. Math.
  Vol.:  179
  Year:  2003
  Pages:   17-25
  Supported by:  IPM
  Abstract:
We prove a convenient equivalent criterion for monotone completeness of ordered fields of generalized power series [[FG]] 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 [[FG]] is always Scott complete. In contrast, the Puiseux series field with coefficients in F always has proper dense field extensions.

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