Timeline for Encoding sets in locally generic sets
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 9, 2018 at 12:02 | vote | accept | M Carl | ||
| Oct 9, 2018 at 10:21 | answer | added | Monroe Eskew | timeline score: 5 | |
| Oct 9, 2018 at 9:52 | comment | added | M Carl | You are right, the question was missing the assumption that $\alpha$ is countable in $L[a]$. Sorry for that. | |
| Oct 9, 2018 at 9:50 | history | edited | M Carl | CC BY-SA 4.0 |
added 44 characters in body
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| Oct 8, 2018 at 19:47 | comment | added | Yair Hayut | I think that I don't understand the question, or that some assumptions are missing: if we take $\alpha = \beta$ to be a regular uncountable cardinal in $L$ then every maximal antichain in $P_\alpha$ in $L$ belongs also to $L_{\beta}[a]$. Thus, $L_\beta[a]$-generic is the same as $L$ generic. If $a$ cannot be added by the Cohen forcing then clearly $a\notin L[x]$ for any $L_\beta[a]$-generic filter $x$. | |
| Oct 8, 2018 at 17:03 | history | asked | M Carl | CC BY-SA 4.0 |