I don't know much about the theory of ordered fields. But I know that, for the real fields 


$\mathbb{R}(y)$, $\mathbb{R}((x))(y)$, and $\mathbb{R}((x))((y))$,


we can explicitly determine all the orderings of the field.


My question: Can we determine all the orderingds of the field $\mathbb{R}((x, y))$?


Can anyone give some brief explanations or a reference? 



orderings of the field R((x, y))
A full description of the orderings of R((x,y)) is given in the paper


Alonso, M. E.(E-MADC); Gamboa, J. M.(E-MADC); Ruiz, J. M.(E-MADC)
On orderings in real surfaces.
J. Pure Appl. Algebra 36 (1985), no. 1, 1–14


In fact this paper describes all orderings of R[[x,y]] in terms of analytic half branches at the origin and the non-algebraic ones correspond to the orderings of R((x,y))


