I am trying to prove the following statement: Given a consistent recursively axiomatizable theory (in a language that only contains one binary relation symbol $R$) then $T$ has a model of the form $(\omega,R)$, where R is $\Delta_{2}$.
To be honest I don't even know how to start to approach this problem, so any hint would be appreciated. I would like also to have any reference to study how to construct this kind of models, or in general, is there any book to understand properly recursively axiomatizable theories? What is known for them? Which kind of models do they have?