Timeline for Large cardinal consistency strength and size
Current License: CC BY-SA 4.0
2 events
| when toggle format | what | by | license | comment | |
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| Sep 23, 2021 at 20:47 | comment | added | Arvid Samuelsson | Actually totally otherworldly cardinals are even $\Sigma_3$-correct. Suppose $\psi = \exists x \forall y \phi(x, y)$ is a $\Sigma_3$ formula (where $\phi$ is $\Sigma_1$). If $\kappa$ is totally otherworldly, there is $\lambda$ such that $V_\kappa \prec V_\lambda$ and there is a witness $x \in V_\lambda$ of $\psi$. Then $\phi(x, y)$ is absolute between $V_\kappa$, $V_\lambda$, and $V$, as noted in this blog post, so $\forall y \phi(x, y)$ is downward absolute and $\psi$ is absolute between $V_\kappa$ and $V_\lambda$ by elementarity. | |
| Sep 11, 2020 at 18:24 | history | answered | Jason Zesheng Chen | CC BY-SA 4.0 |