Approximation properties for orderings on *-fields

Abstract

The goal of this paper is to extend the main theorems on approximation properties of the topological space of orderings from formally real fields to skew fields with an involution ∗ ^{\ast } . To accomplish this, the concept of ∗ ^{\ast } -semiordering is developed and new theorems are obtained for lifting ∗ ^{\ast } orderings from the residue class field of a real valuation.