# Questions tagged [provability]

For questions on provability, the capability of being demonstrated or logically proved.

151 questions
75 views

### ZFC,unprovability of existence of a countable model,Skolem construction and paradox

The well-known Skolem construction yields a countable model of ZFC,elemetarily equivalent to the universe of sets $V$.Why this construction is not a proof of existence of models of ZFC,as such proofs ...
518 views

### On provability of Paris–Harrington theorem

It is said that the Paris–Harrington theorem is true, but not provable in Peano arithmetic. I want to ask: So how do they know that it is true if it has no proof? I cannot imagine someone knows ...
254 views

### A few questions about a true but unprovable statement

Can someone explain to me what this comment means: If ZFC is not a sound theory, a true but unprovable statement may be refutable and therefore decidable. What is a sound theory? What is meant ...
140 views

Suppose we have some random phenomena. Is it true that any event concerning the phenomena has a fixed "correct" probability? That is, the correct probability is the relative number of occurrences of ...
910 views

### Difference between 'true' and 'provable'

For a long time now I've been confused about the difference between truth and provability. I've also read questions like this but I still don't understand it. A typical example of my confusion is the ...
51 views

### provability of a mathematical statement

Is it possible to prove that a non-axiom statement is not mathematically provable with current accepted axioms of mathematics? Note that this is not a question of proving if it is a true or false ...
106 views

### Is this a valid logical paradox?

In some recent cases, I have noticed some theorems are accepted to be intuitively or logically true if they themselves, as a unit, have no valid proof, but, their statements can be used to prove ...