Timeline for How can we know the well-foundedness of $\epsilon_0$?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 23, 2020 at 14:42 | vote | accept | Paul Sohn | ||
| Apr 23, 2020 at 13:59 | answer | added | Andreas Blass | timeline score: 14 | |
| Apr 23, 2020 at 11:18 | comment | added | Paul Sohn | @godelian Not exactly. I've read the article a month ago. Perhaps I skimmed a lot, but I couldn't get any information further than "$PRA+WF(\epsilon_0)$ is neither stronger nor weaker than $PA$, and it proves $Con(PA)$." No claim that $WF(\epsilon_0)$ actually holds for the natural numbers. | |
| Apr 23, 2020 at 11:01 | comment | added | Paul Sohn | @Wojowu Actually I mentioned in OP about second-order scheme and I'm not satisfied with it. I believe that proving something with second-order arithmetic is technically equivalent to proving it with a set theory, which must be backed up with a first-order characterization such as ZFC. | |
| Apr 23, 2020 at 10:30 | comment | added | godelian | Timothy Chow has written an expository article on the consistency of arithmetic and the induction up to $\epsilon_0$. It appeared in the Mathematical Intelligencer (timothychow.net/consistent.pdf). Maybe he can say something about this. | |
| Apr 23, 2020 at 10:19 | comment | added | Wojowu | Second-order arithmetic can prove $WF(\varepsilon_0)$ too. | |
| Apr 23, 2020 at 10:09 | review | First posts | |||
| Apr 23, 2020 at 10:51 | |||||
| Apr 23, 2020 at 10:02 | history | asked | Paul Sohn | CC BY-SA 4.0 |