“School of Mathematics”
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| Paper IPM / M / 2355 |
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| Abstract: | |||||
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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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