Timeline for Why is a Boolean algebra being $\kappa$-saturated upward closed in $\kappa$?
Current License: CC BY-SA 4.0
4 events
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| May 25, 2022 at 12:20 | comment | added | Andreas Lietz | Yes, you're right Gabe! Maybe I should post this as an answer... | |
| May 23, 2022 at 20:20 | comment | added | Gabe Goldberg | @AndreasLietz This answers the original question, right? You've produced a Boolean algebra with no partition of size $\omega$ that does have a partition of size $\omega_1$. | |
| May 23, 2022 at 10:15 | comment | added | Andreas Lietz | While $B$ and its completion have the same cardinalities of antichains, they might not have the same cardinalities of maximal antichains, which is what one would need here as a partition is just a maximal antichain. For example the Boolean algebra given by the finite, cofinite subsets of $\omega_1$ has no maximal antichain of size exactly $\omega$ while its completion, the whole powerset of $\omega_1$, certainly does. | |
| May 21, 2022 at 2:09 | history | answered | Chad Groft | CC BY-SA 4.0 |