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 ...