Timeline for Regarding Gentzen's note regarding 'Godel-points' (i.e., "Where is the Godel-point hiding?")
Current License: CC BY-SA 4.0
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| Oct 9, 2019 at 6:44 | history | edited | Panu Raatikainen | CC BY-SA 4.0 |
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| Oct 8, 2019 at 21:46 | comment | added | Thomas Benjamin | the last sentence should read: Why doesn't Gentzen's note 'draw blood'? | |
| Oct 7, 2019 at 21:47 | comment | added | Thomas Benjamin | (cont.) the case (as does (Zach) of such transfinite induction's 'finitariness'. Take a look (for the umpteenth time, no doubt) at the Peano Axioms--they seem to be 'obvious' statements derived from the definition of the operations and relations. Why doen Gentzen's not 'draw blood'? | |
| Oct 7, 2019 at 21:43 | comment | added | Thomas Benjamin | Thanks for your helpful answer--it is somewhat closer to the mark (so to speak) especially considering that you note (in your 'Stanford' entry) that transfinite induction up to $\epsilon_0$ in an early example on an unprovable mathematical statement on a par (so you wrote in your entry) with Paris-Harrington (and others). If one assumes $\epsilon_0$ exists (and if one assumes $\omega$ exists, why not....) then transfinite induction up to $\epsilon_0$ is 'true' but unprovable. If one uses Gentzen's (or Hilbert-Bernays', or Ackermann's) ordinal notations, one can even make | |
| Oct 7, 2019 at 19:13 | history | edited | Panu Raatikainen | CC BY-SA 4.0 |
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| Oct 7, 2019 at 19:07 | history | answered | Panu Raatikainen | CC BY-SA 4.0 |