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Out of curiosity, could you give some examples of such theorems?



1. The original example would be Goedel's own example, namely, the statement (formulated in the language of PA) that PA is consistent, i.e., that PA does not prove 1=0.

Less contrived examples are:

2. Goodstein's Theorem https://en.wikipedia.org/wiki/Goodstein%27s_theorem

3. A theorem stating that every computable strategy is a winning strategy in the hydra game (see https://faculty.baruch.cuny.edu/lkirby/accessible_independen...)

4. The strengthened finite Ramsey theorem, see https://en.wikipedia.org/wiki/Paris%E2%80%93Harrington_theor...


Thanks!




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