Specific cases of this theorem are much easier to prove if the theory satisfies three conditions named for Hilbert, Bernays, and Löb.
Specific cases of this theorem are much easier to prove if the theory satisfies three conditions named for Hilbert, Bernays, and Löb. One lemma used in the proof of this statement claims that for any function, there exists a sentence that implies that function taken on the number of the sentence; that is the diagonalization lemma. The proof of this theorem involves uniquely encoding all statements in a theory in its formulator's namesake numbers, and then constructing a (*) self-referential statement. This theorem states that any sufficiently strong theory will have statements that are true but unprovable. For 10 points, name this pair of theorems about the limitations of the foundations of mathematics, proven by Kurt Gödel.
Specific cases of this theorem are much easier to prove if the theory satisfies three conditions named for Hilbert, Bernays, and Löb.
Gödel's incompleteness theorems (accept "first" or "second" before "incompleteness theorem")