to an ordering on a field? up vote 0 down vote favorite If $(K,\leq)$ is a totally ordered field with $P\!=\!\{\alpha\!\in\!K;\, 0\!\leq\!\alpha\}$, how is the valuation associated to $P$ defined? I was searching through Prestel & Delzell's Positive Polynomials and Engler & Prestel's Valued Fields , but didn't find anything. Perhaps