Timeline for Which cardinal $\kappa\geq \omega_1$ is critical for the following property...?
Current License: CC BY-SA 4.0
8 events
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| Mar 9, 2023 at 10:04 | comment | added | Boaz Tsaban | I think you should refrain from using the word "critical cardinality", and provide a precise definition of kappa. I guess you mean the minimal cardinal such that the property you describe fails for some space of cardinality kappa. Make this precise. | |
| Jan 27, 2023 at 5:06 | review | Close votes | |||
| Feb 9, 2023 at 3:09 | |||||
| Jan 27, 2023 at 4:37 | comment | added | Alexander Osipov | perhaps a revised version of the question would be more clear | |
| Jan 27, 2023 at 4:36 | history | edited | Alexander Osipov | CC BY-SA 4.0 |
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| Jan 27, 2023 at 0:18 | comment | added | Asaf Karagila♦ | Critical? What do you mean? | |
| Jan 26, 2023 at 20:21 | comment | added | Joel David Hamkins | If it is true for $\kappa$, then isn't it also true for any smaller $\kappa$, including $\kappa=\omega_1$? Given any set of size $\omega_1$, first extend it to a set of size $\kappa$, get the $X_\alpha$'s, and then cut back down to the original set. Or have I misunderstood? Oh, maybe when you cut down, you get some $X_\alpha$ becoming countable...is that the issue? | |
| Jan 26, 2023 at 19:21 | history | edited | Alexander Osipov | CC BY-SA 4.0 |
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| Jan 26, 2023 at 19:09 | history | asked | Alexander Osipov | CC BY-SA 4.0 |