The number fields that are O*-fields II

Abstract

An O* -field is a field K for which each partial order with respect to which K is a partially ordered field can be extended to a total order with respect to which K is a totally ordered field. When F is an even finite-dimensional extension field of ℚ contained in ℝ, necessary and sufficient conditions are found for F to be an O* -field. Examples are provided to illustrate how the results can be used. This paper continues previous work of Ma.