Timeline for Are all "reasonable" Gödel encodings isomorphic in some sense?
Current License: CC BY-SA 4.0
4 events
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| Feb 6 at 5:13 | comment | added | Joshua Grochow | @NoahSchweber: I admit I didn't quite follow all of that, but it sounds plausibly like what I was hoping for, so I would certainly appreciate reading more details about it! | |
| Feb 6 at 3:32 | comment | added | Noah Schweber | In particular, if $\Phi,\Psi$ are the interpretations corresponding to two "reasonable" Godel numberings, there is a formula $\theta$ such that in every $\mathcal{M}\models\mathsf{PA}$ we have $\theta^\mathcal{M}:\Phi^\mathcal{M}\cong\Psi^\mathcal{M}$. Is this the sort of situation you're looking for? If so, I can expand this into an answer. | |
| Feb 6 at 3:31 | comment | added | Noah Schweber | We can whip up a theory $T$ describing numbers-sentences-formulas-etc. (think of it as a "theory of syntax") such that every "reasonable" Godel numbering scheme is essentially describing an interpretation $\Phi$ of $T$ into $\mathsf{PA}$ such that for every $\mathcal{M}\models\mathsf{PA}$ the interpreted structure $\Phi^\mathcal{M}$ uniquely embeds into any other model of $T$ definable in $\mathcal{M}$ (basically, $\Phi^\mathcal{M}$ is what $\mathcal{M}$ thinks is the minimal model of $T$). (Cont'd) | |
| Feb 5 at 23:14 | history | asked | Joshua Grochow | CC BY-SA 4.0 |