Timeline for How do these two principles of Foundation written in $\mathcal L_{\omega_1,\omega}$ compare?
Current License: CC BY-SA 4.0
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| Jun 15, 2023 at 12:18 | comment | added | Zuhair Al-Johar | So your answer is that both versions of Foundation are equivalent. Can you clarify how we can use $\phi$ to create the counter-example in the first argument of yours? I mean you need to prove that sequence to be a set, for it to violate ZFC foundation (i.e. the usual one in $\mathcal L_{\omega,\omega}$), isn't it? Note that $\phi$ may not be written in $\mathcal L_{\omega,\omega}$. | |
| Jun 15, 2023 at 6:13 | history | edited | Holo | CC BY-SA 4.0 |
added 146 characters in body
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| Jun 14, 2023 at 14:01 | comment | added | Holo | @ZuhairAl-Johar you are correct, I misread the definitions, I'll edit my answer when I get home | |
| Jun 14, 2023 at 11:58 | history | answered | Holo | CC BY-SA 4.0 |