[FOM] Order types of ordered fields

[Alasdair Urquhart]

I have a copy of Joseph Rosenstein's book 
"Linear Orderings" that has
a few results on this.  On p. 126, 
Rosenstein observes that the order type
of any ordered fields is doubly transitive.
On the other hand, the order type of the
irrationals, although doubly transitive, 
is not the order type of any
ordered field, as follows from Rosenstein's
Theorem 8.15 (pp. 126-127).

However, Rosenstein's book is from 1982,
so perhaps there has been progress since
then.  Does any FOM subscriber have
information?