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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.
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