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Any references would be appreciated. Most places only address different vocabularies (e.g. a survey of arithmetical definability by Bes).

I'm working on my thesis about Gödel's Incompleteness Theorems, and at some point I need to prove that the $\textsf{PA}$ system is able to represent all the recursive functions. By recursive function ...

It is a well-known fact that while while Robinson arithmetic can interpret surprisingly strong theories, it cannot interpret $\mathsf{I}\Delta_0 + \mathrm{Exp}$, i.e., Peano arithmetic with induction ...

Begin with a bit of notation. Let $t = t_0, \ldots, t_d$ be a finite sequence of real numbers. Define $$\lambda^t(x) = x^{t_0} \log(x)^{t_1} \log(\log(x))^{t_2} \cdots.$$ for all real numbers $x \in ...