Sentence examples for are provable from inspiring English sources

As a consequence, this also settles Henkin's original problem: assuming that the arithmetized provability predicate is again "normal" (i.e., satisfies Löb's derivability conditions), all sentences "asserting their own provability" are provable.

Detlefsen argues that these conditions are not necessary for a predicate to count as a genuine provability predicate, and indeed there are provability predicates which violate the provability conditions and which give rise to consistency formulas which are provable in their corresponding theories.

The answer is unfortunately a resounding no: Vardanyan (1986) has proved on the basis of ideas by Artemov (1985) that the set of sentences of predicate provability logic all of whose realizations are provable in PA is not even recursively enumerable, so it has no reasonable axiomatization.

But they are provable untruths.

None of their theories are provable, but all are plausible.

Like him, I can't think of any that are provable.

Leon Henkin put forward the question whether the sentence expressing its own provability ("I am provable") is true or false, and provable or not (Henkin 1952).

Heyting also proposes a provability operator +, where +p means "p is provable".

Hence, if the arithmetic sentence were provable, p would also be provable contradicting the previous result.

Soundness: if something is provable, it is valid.

The truth is plain, and it is provable.