Timeline for answer to Image-catching families in $\omega$ by Farmer S
Current License: CC BY-SA 4.0
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6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 29, 2024 at 8:21 | vote | accept | Dominic van der Zypen | ||
| Jul 28, 2024 at 3:23 | comment | added | Farmer S | Now with a ZFC version. | |
| Jul 28, 2024 at 3:22 | history | edited | Farmer S | CC BY-SA 4.0 |
added 8159 characters in body
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| Jul 28, 2024 at 2:48 | comment | added | Dominic van der Zypen | Very nice answer, thanks FarmerS! If I understand correctly, then under MA (and also, trivially, CH) every image-catching family had cardinality $\frak c$, but we don't know yet whether this is provably true in $\sf (ZFC)$. Di I wait a short time before accepting the answer if this is okay for you | |
| Jul 27, 2024 at 21:39 | comment | added | bof | And the argument from CH or MA still works if the condition "there are $C,D\in\mathcal C$ such that $\varphi(C)=D$" is weakened to "there are $C,D\in\mathcal C$ such that either $\varphi(C)\subseteq D$ or else $\varphi(C)\supseteq D$," or even "there are $C,D\in\mathcal C$ such that either $\varphi(C)\setminus D$ or $D\setminus\varphi(C)$ is finite." Right? | |
| Jul 27, 2024 at 13:19 | history | answered | Farmer S | CC BY-SA 4.0 |