Timeline for Consistency of the size of the least real-valued measurable cardinal, vis-a-vis the continuum
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 3, 2018 at 2:30 | vote | accept | Zoorado | ||
| May 2, 2018 at 23:12 | answer | added | Robert Furber | timeline score: 3 | |
| May 2, 2018 at 16:55 | comment | added | Jing Zhang | I think the following works: Let $\kappa$ be the least measurable cardinal in $V$. For 1), take $\lambda>\kappa$ such that $\lambda^\omega=\lambda$, then adding $\lambda$ many random reals will produce $2^\omega=\lambda$ and $\kappa<\lambda$ is real-valued meas. For 2), you can start with $V=L[U]$ and choose $\lambda=\kappa$ as in the first case. If there is a real-valued meas below $\mathfrak{c}=\kappa$ I think you produce an inner model of measurable cardinal $<\kappa$, this will contradicts uniqueness. For 3), any model of CH works. | |
| May 2, 2018 at 14:17 | history | asked | Zoorado | CC BY-SA 4.0 |