All Questions

Below, I use the term "tracker" rather than "realizer" since I'm not requiring the relevant objects to be computable. Define the relation "$f$ tracks $\varphi$" for $f:\...

I just read Dunn's 1979 paper Relevant Robinson's Arithmetic, and the end especially caught my interest. Following the surprising role of constant functions in collapsing "relevant Q with zero&...

Does anyone know whether the following hierarchy of fragments of $\mathrm{I} \Sigma_1$ (or rather $\mathrm{I} \Pi_1$) collapses or not? Let $\Sigma^b_n$ denote formulas in the language of arithmetic ...

It is known that there are a number of expansions of the structure $\mathfrak{N}:=(\mathbb{N};+)$ which are decidable (= have computable theories); one such example is the expansion by a predicate ...

Let $PA_{\omega}$ be just like $PA$ except that $PA_{\omega}$-proofs can use any number of applications of the recursive $\omega$-rule. The recursive $\omega$-rule allows the following: For each ...