Timeline for Why is it OK to rely on the Fundamental Theorem of Arithmetic when using Gödel numbering?
Current License: CC BY-SA 4.0
5 events
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| Apr 10, 2024 at 12:31 | history | edited | Martin Sleziak | CC BY-SA 4.0 | a minor typo |
| Jan 31, 2011 at 15:58 | comment | added | Timothy Chow | Feferman proves a version of the second incompleteness theorem in his system $FS_0$: Finitary inductively presented logics I don't think $FS_0$ is weaker than $\Sigma_1$ induction though. | |
| Jan 30, 2011 at 23:12 | comment | added | Carl Mummert | I learned only recently that Pudlak proved in 1985, by model-theoretic techniques, that Q does not prove Con(Q), along with finer results. This is in the paper "Cuts, consistency statements and interpretations" from the JSL volume 50. I don't think that anyone has proved a sort of reverse-mathematics result that characterizes the amount of induction required to verify the Hilbert-Bernays conditions. $Sigma^0_1$ induction is certainly enough, but I don't remember about weaker theories at the moment. | |
| Jan 29, 2011 at 20:59 | comment | added | Andrés E. Caicedo | @Andreas , do you know of a reference that pursues the question of how little/much of PA is actually required? I seem to recall "Metamathematics of first order arithmetic" treats some of this, but don't recall the explicit suggestion that $\Sigma^0_1$ induction seems enough (I do not have the book with me, though, so I cannot currently check). | |
| Jan 29, 2011 at 8:03 | history | answered | Andreas Blass | CC BY-SA 2.5 |