Timeline for What is the consistency strength of $L(\mathbb{R})\models$ "$\omega_1$ has tree property"?
Current License: CC BY-SA 4.0
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| 6 hours ago | comment | added | Farmer S | Yes, it does seem to work in that generality. | |
| 6 hours ago | comment | added | new account | Thanks a lot. I should have tried this before posting the question...Is there a "metatheorem" on the sort of large cardinal properties that can be transferred to $\omega_1$? According to this answer, Jech's construction works for any large cardinal property that is preserved under small forcing and is of the form $\forall X\exists Y\ \phi(X,Y)$, where $\phi$ is something upward absolute. Your argument seems to work in this generality too? | |
| 7 hours ago | vote | accept | new account | ||
| 7 hours ago | history | answered | Farmer S | CC BY-SA 4.0 |