Timeline for Antichain on $\mathcal{P}(\omega)/fin$ of cardinality $2^{\aleph_0}$?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 20, 2018 at 15:04 | comment | added | KP Hart | Or follow Sierpinski and define the sequence explicitly for irrational $r>1$: let $r_n=\frac1n\lfloor nr\rfloor$ | |
| Mar 31, 2015 at 13:09 | comment | added | Asaf Karagila♦ | @Andreas: Ha! It didn't even cross my mind. Thanks! | |
| Mar 31, 2015 at 13:06 | comment | added | Andreas Blass | It might be worth pointing out that this example works whether you use the set-theorist's definition of antichain (pairwise incompatible) or everybody else's definition (pairwise incomparable). If you wanted only the latter, weaker sort of antichain, you could take the sets $\{k:r<q_k<r+1\}$ for all reals $r$. | |
| Mar 23, 2015 at 14:41 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 |
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| Mar 23, 2015 at 14:39 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 |
added 88 characters in body
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| Mar 23, 2015 at 9:08 | vote | accept | Dominic van der Zypen | ||
| Mar 23, 2015 at 8:42 | history | answered | Asaf Karagila♦ | CC BY-SA 3.0 |