Timeline for A question on cofinite topology.
Current License: CC BY-SA 3.0
7 events
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| Apr 24, 2013 at 3:25 | vote | accept | Empty.Subset | ||
| Apr 23, 2013 at 19:24 | comment | added | Joel David Hamkins | In particular, since for Dedekind finite sets one can find $\xi$ of cardinality strictly smaller than $X$, we do know that some AC is involved in the claim that all such $\xi$ have the same size as $X$. | |
| Apr 23, 2013 at 17:42 | comment | added | Joel David Hamkins | Yes, I agree with all that. | |
| Apr 23, 2013 at 17:38 | comment | added | Asaf Karagila♦ | Andreas, that is an interesting question. My intuition points to "there is no minimal cardinality". | |
| Apr 23, 2013 at 17:34 | comment | added | Andreas Blass | Since you only need to intersect co-singletons, your $\xi$ can have cardinality at most that of $X$ even without AC. If you you want $\xi$ to have exactly the cardinality of $X$, even if $X$ is Dedekind-finite, then just throw one more set into $\xi$. An interesting question might be, in the Dedekind-finite case, how much smaller than $X$ you can make $\xi$. | |
| Apr 23, 2013 at 13:10 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 369 characters in body
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| Apr 23, 2013 at 13:04 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |