The word "provable" is correct and can be used in written English.
You can use it when referring to something that has been proven to be true, or that can be readily demonstrated or shown to be true. For example, "The claims made by the company have not yet been provable."
The difference between the two notions of provability: "provable in a given formal system S" and provability by any correct means — manifests itself as a consequence of Gödel's Second Incompleteness Theorem, as follows.
In particular, although the specific accusations made by Mr Gilligan do not stand up, the more general, but less provable, charge that Tony Blair exaggerated the threat from Iraq still stands.Yet even this story is not as simple as the prime minister's critics maintain.
Yet despite an outcry, the policeman has so far been punished with nothing worse than paid leave.Picture the differenceTo have real clout, video evidence needs not only clarity and impact but also provable authenticity, notes Sam Gregory of Witness, a human-rights group that promotes the use of video.
Much of what is now coming out about corruption in the Sanader years was widely known beforehand but not provable.
Until then, I remain, like most doctors, sceptical.DR RAJ PERSAUDLondonSIR You clearly share the conventional medical view that if an approach doesn't have an accepted or "provable" theoretical underpinning, there is no point in examining whether it is effective or not.
Then (6) states a provable principle.
This principle is provable in Peano Arithmetic.
Thus, AC is not provable in Q0.
This last sentence is then provable.
If an underlying paraconsistent logic is used to formalise the arithmetic, and the theory therefore allowed to be inconsistent, the Gödel sentence may well be provable in the theory (essentially by the above reasoning).
If G is provable, then it is true and so not provable.
