Formally real field
= Formally real field
{title2=$-1\ne\sum_{j=1}^m a_j^2$}
{wiki}
A <field> is formally real when $-1$ is not a finite sum of squares. The <Artin-Schreier ordering criterion> says this is equivalent to the existence of an ordering compatible with the field operations. Such a field has characteristic zero and embeds into a <real closed field>.