Superreal field

This article defines a field property: a property that can be evaluated to true/false for any field.
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Definition

A superreal field is a field isomorphic to the field of fractions of an integral domain of the form $C(X)/P$, where $X$ is a completely regular space, $C(X)$ is the ring of continuous real-valued functions on $X$, and $P$ is a prime ideal in $C(X)$.