Timeline for On self-reference in a weak structure
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Sep 18, 2023 at 3:01 | history | bounty ended | CommunityBot | ||
| S Sep 18, 2023 at 3:01 | history | notice removed | CommunityBot | ||
| Sep 13, 2023 at 2:09 | comment | added | Noah Schweber | @JamesHanson Pretty much! | |
| Sep 13, 2023 at 2:07 | comment | added | James E Hanson | Right, because for starters you're only talking about a single formula at a time (although requiring uniformity in parameters). Basically, you're asking about which formulas the diagonal lemma does hold for in $(\mathbb{N};+)$. It's just that this is technical to formalize because we don't necessarily have enough machinery for a uniform system of Gödel numbers. Would you say this is accurate? | |
| Sep 13, 2023 at 2:04 | comment | added | Noah Schweber | @JamesHanson I think that's more high-powered than what I'm talking about here. | |
| Sep 13, 2023 at 2:04 | comment | added | James E Hanson | Oh I see. I meant the fact that you can define $\Sigma^0_n$ truth predicates for each $n$. | |
| Sep 13, 2023 at 2:01 | comment | added | Noah Schweber | @JamesHanson I don't know what a "local truth predicate" is, so probably not. The point is just that (in $(\mathbb{N};+,\times)$) we can definably-in-the-Godel-numbering $\#$ produce, for any arithmetic formula $\varphi$, a sentence $\theta_\#$ satisfying $$(\mathbb{N};+,\times)\models \theta_\#\leftrightarrow\varphi(\#(\theta_\#))$$ (conflating numbers and numerals here for simplicity). | |
| Sep 13, 2023 at 1:58 | comment | added | James E Hanson | Am I understanding correctly that the point is that $\mathsf{SR}(\mathcal{A})$ is supposed to abstract the 'local truth predicates' that are definable in $(\mathbb{N};+,\times)$? | |
| S Sep 10, 2023 at 1:48 | history | bounty started | Noah Schweber | ||
| S Sep 10, 2023 at 1:48 | history | notice added | Noah Schweber | Draw attention | |
| Aug 28, 2023 at 4:29 | history | asked | Noah Schweber | CC BY-SA 4.0 |