All Questions

Recall that a set $A \subseteq \mathbb N$ is (many-one, Turing) $\Sigma_n$-complete if it's $\Sigma_n$ and any other $\Sigma_n$ set (many-one, Turing) reduces to it. This definition actually makes ...

There is a natural analogy between the theories PA and ZFC. See the linked question by Gro-Tsen here. Peano arithmetic (PA) is a first order approximation to the natural numbers. As is well known, ...

The following question is about patterns of synonymy relationships around two theories, $T^+$ and $\sf PA$. For purposes of self inclusiveness I'll re-iterate $T$ and its extensions. $\textbf{Logic:}$ ...