# quote marks should look like this'', because this" doesn't work with latex2html

As it turns out, a field endowed with a pre-positive cone has an order structure. The field is called a formally real, orderable, or ordered field. Before defining what this order" is, let's do some preliminary work. Let $P_0$ be a pre-positive cone of a field $F$. By Zorn's Lemma, the set of pre-positive cones extending $P_0$ has a maximal element $P$. It can be shown that $P$ has two additional properties:

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