Formally real field

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2020 Mathematics Subject Classification: Primary: 12J15 [MSN][ZBL]

A field $F$ which is capable of being made an ordered field. The existence of such an order is equivalent to the property that $-1$ is not a sum of squares in $F$: this is the Artin--Schreier theorem. A real closed field is a formally real field for which no algebraic extension is formally real.


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