All Questions

Let $\mathcal{L}$ be a recursive first-order theory, with a deductive system $\Xi$ (for instance, Hilbert-Ackerman proof system). Let $\phi$ be a formula and let $l=(\psi_1, \ldots, \psi_n=\phi)$ be a ...

I'm trying to get a deeper understanding of Buss's version of Gödel's speedup proof. In short, if we assume that $Z_0$ is first-order arithmetic, $Z_1$ is second-order arithmetic, and so on, then for $...

Before formulating my question, let me briefly sum up what I know about the topic (feel free to correct me if something I claimed is false!). This is for you good to see what my state of knowledge is, ...

The notion of formal proof is defined by finite sequences ($<\omega$ - sequences) of sentences. In some sense if a sentence $\sigma$ is (finitely) provable from the theory $T$ it is very "near" to ...

Is there any recursively axiomized system with infinitely many proofs for some propositions or a proposition? So we will have at least one proposition which is deduced from the recursively axiomatic ...