In the paper "A Non-Standard Model for a Free Variable Fragment of Number Theory", Shepherdson constructs a recursive model for a fragment of arithmetic known as "Open Induction". I would like to learn the construction but the paper seems hardly available. Does anyone knows where the paper can be found or does anyone knows an alternative (available) source in which the Shepherdson-construction is explained?
What I have found out so far is that the following theorem seems essential for the construction of Shepherdson's model:
$\textbf{Theorem.}$ Let $R$ be a discretely ordered ring and let $F$ denote the real closure of its field of fractions. Then, $R$ is a model of open induction iff $R$ is an integral part of $F$.
I did not found a source containing the proof of this theorem, so I am trying to prove it by myself but I have no idea where to start. It will also be helpful to me if someone can provide me some hints or a sketch of the proof (presupposed it is not too long and complicated to be stated here). Thanks in advance!