Alternate orders on subfields of the real numbers (Q1978829)

This is an abstract of a talk based on a joint work of \textit{G.~P.~Barker, L.~Eifler, J.~Foran} and \textit{E.~Pirtle.} The authors are interested in the problem of finding a subfield \(T\) of the real line which would have more than one order which turns \(T\) into an ordered field. In fact, for any cardinal \(m\leq \mathbb C = 2^{\omega _0}\), the authors find a subfield \(T\) with \(2^m\) such orders.