Timeline for Given an elementary embedding $j: M\to N$ and a strong master condition $q\in N$, how are we able to construct a generic over $M$ from $M$?
Current License: CC BY-SA 4.0
6 events
when toggle format | what | by | license | comment | |
---|---|---|---|---|---|
Mar 12, 2023 at 10:16 | comment | added | Monroe Eskew | I don’t see any way to show it in general besides noting that generic filters for nontrivial forcings don’t exist (in the ground model). | |
Mar 12, 2023 at 10:06 | vote | accept | Connor W | ||
Mar 12, 2023 at 10:06 | comment | added | Connor W | Thanks, Monroe. Is there a more direct way to see that a strong master condition can't exist for a definable class embedding? I don't mean directly in the precise sense, I mean an argument which refers to the actual embedding and poset, rather than a "Oh, if there were a strong master condition, then you could build an $M$-generic internally." Or, at least, some intuitive reasoning. (By the way, I notice in your first sentence that you don't mention definability, where I actually use this in my argument. Is this not necessary for the nonexistence of a strong master condition?) | |
Mar 12, 2023 at 9:55 | comment | added | Monroe Eskew | Yes, lifted through G. | |
Mar 12, 2023 at 9:13 | comment | added | Connor W | To clarify, at the end, when you say that $q$ is a strong master condition for $j$ and $\mathbb{Q}$, is this $j$ the lifted embedding? | |
Mar 12, 2023 at 9:01 | history | answered | Monroe Eskew | CC BY-SA 4.0 |