On Quasi-ordered fields with a view towards algebraic and model theoretic applications

In 1987, Syed M. Fakhruddin introduced the notion of quasi-ordered fields and showed that any such field is either an ordered field or a valued field. In this talk we briefly sketch the proof of Fakhruddin's result. Afterwards we demonstrate with examples from real algebra and model theory how via quasi-ordered fields, the theories of ordered and valued fields can be unified.