# Tagged Questions

For question in Proof Theory, where "proofs" themselves are the object of mathematical investigation. It is not to be used to request a proof of some result.

58 views

### Prove in GL that no statement can be proven consistent with PA unless PA is inconsistent [closed]

Edit: I moved this question to math.stackexchange.com here as sugested. I'm trying to do a exersie on page 16 of this paper. It says: Exercise. Show, using the rules of Godel-Lob modal logic ...
168 views

### Adding a truth-like predicate to PA

It is well known that adding a truth predicate to arithmetic in the most natural way leads to a contradiction. Suppose as usual that we add a one place relation T to the language of arithmetic, and ...
137 views

### Set theory and forcing from the point of view of a formal system $G^+$ of Gentzen type

There are four papers by Vladimir Alfeevich Kuznetsov, which discuss the above titled topic: (1) Some problems in set theory from the standpoint of a formal system G+ of Gentzen type. (Russian) Akad. ...
141 views

### Reducing Consistency of $PA$ [closed]

By godel translation consistency of $PA$ is equivalent to consistency of $HA$. I want to know any similar theorems for $PA$. 1.What is the minimal theory $T\subsetneq PA$ such that the proof of ...
259 views

### Intutionistic Robinson Arithmetic

By Friedman translation $HA$ and $PA$ prove the same $\Pi_2$ formulas. Is it true for Intutionistic Robinson arithmetic(Robinson axioms with intutionistic logic) and classic Robinson arithmetic? ...
133 views

### Why is a cut-free system consistent?

Assume that the cut-elimination theorem holds for a system $T$. Then, for any proof that makes use of the cut-rule in $T$, there is a proof that does not make use of the cut-rule. An immediate ...
207 views

### How do I evaluate this sum for $s$ is a complex variable :$\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^{2s}n!}$?

This question related to this question in SE ,I would like to know how do I evaluate this sum for $s$ is a complex variable :$$\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^{2s}n!}$$ . Edit01:And I think ...
374 views

### Algorithmic complexity of formal proof verification?

In this question, suppose $S$ is some popular real-world automated proof system that is stronger than or equivalent to Peano Arithmetic. I would be happy with a positive answer to the following for ...
1k views

### Euler's constant: irrationality and proof theory

Let γ represent Euler's constant. Is there a real number x such that there is a proof within Zermelo-Fraenkel set theory (ZF) that x is irrational and there is also a proof within ZF that γ + x is ...
62 views

535 views

### Why is there no connection between fast-growing functions and complex analysis

I found myself wondering the other day whether the fast-growing functions from natural to naturals that are studied by people like proof theorists are the restriction to the naturals of analytic ...
254 views

### what are the proof-theoretic ordinals of second-order arithmetic and ZFC? [duplicate]

are they still smaller than omega-1-CK?what are the notations of them?