4 ms·
Out of curiosity, could you give some examples of such theorems?
by strbean 7y ago
Out of curiosity, could you give some examples of such theorems?
- xamuel 7y ago1. 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 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_independence_results.pdf https://faculty.baruch.cuny.edu/lkirby/accessible_independen...) 4. The strengthened finite Ramsey theorem, see https://en.wikipedia.org/wiki/Paris%E2%80%93Harrington_theorem https://en.wikipedia.org/wiki/Paris%E2%80%93Harrington_theor...
- strbean 7y agoThanks!