Timeline for How complete is $\mathcal P(\kappa)/J_{bd}$?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 15, 2013 at 19:21 | vote | accept | Asaf Karagila♦ | ||
| Aug 30, 2013 at 21:41 | answer | added | Monroe Eskew | timeline score: 6 | |
| Aug 30, 2013 at 3:54 | answer | added | Garrett Ervin | timeline score: 4 | |
| Aug 29, 2013 at 18:42 | comment | added | Asaf Karagila♦ | Thanks Paul, that's quite helpful. This seems to be easily generalized to large cardinalities. Moreover if we take $A'_n=A_1\cup\ldots\cup A_n$ then we get the same result for an increasing sequence, so both my questions have a negative answer. (Nice seeing you here, by the way!) | |
| Aug 29, 2013 at 18:03 | comment | added | Paul McKenney | You don't need a gap to show that suprema don't exist in $\mathcal{P}(\omega)/\mathrm{Fin}$; take any sequence $A_n$ ($n < \omega$) of pairwise-disjoint, infinite subsets of $\omega$. If $A$ is a $\subseteq_*$-upper bound for this sequence, then one can find $B\subseteq A$ such that $A\setminus B$ is infinite and $B$ is still an upper bound, by removing one element from each intersection $A\cap A_n$ . Hence the sequence $A_n$ ($n < \omega$) has no least upper bound. | |
| Aug 29, 2013 at 8:46 | history | asked | Asaf Karagila♦ | CC BY-SA 3.0 |