On archimedean fields (Q1021360)

In this note 18 necessary and sufficient conditions for a formally real field \(K\) are established such that \(K\) admits only Archimedean orderings. Some of them are well-known. These conditions are given in connection with real valued places of \(K\), the order topology \(\mathcal T\), the completion \(K^*\) of \(K\) with respect to \(\mathcal T\), or convex bodies in the vector space \(K_F\) over an ordered subfield \(F\subset K\). Some of these properties will be generalized for fields \(K\) with a partial order for which all compatible orders are Archimedean.