Timeline for Products of Cohen forcings
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 19, 2015 at 13:57 | history | edited | Yair Hayut | CC BY-SA 3.0 |
removing too optimistic generalization
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| Jan 19, 2015 at 13:48 | comment | added | Monroe Eskew | It is open whether dense ideals can exist on successive cardinals. If we skip cardinals we can get them on $\omega_1$, $\omega_3$, $\omega_5$, etc. It is also open whether dense ideals can exist at successors of singulars, though it is known to contradict SCH. This is discussed in my thesis, and it is a problem I would like to make progress on. | |
| Jan 19, 2015 at 13:44 | comment | added | Yair Hayut | @Monroe: You're right! So it seems like I really need a dense ideal. Is it consistent that such ideals exist for every regular cardinal? | |
| Jan 19, 2015 at 13:27 | comment | added | Monroe Eskew | It's not true that the symmetric difference between two sets in $\mathcal F_\gamma$ is in $I$. By definition, it just means that the intersection of two sets from that filter is in $I^+$. But the difference can be in $I^+$ as well. | |
| Jan 19, 2015 at 12:49 | comment | added | Yair Hayut | @MonroeEskew I edited the answer. I hope that it is clearer now. I must admit that the distinction between centerness and density confuses me and I don't really understand the difference in this case. | |
| Jan 19, 2015 at 12:45 | history | edited | Yair Hayut | CC BY-SA 3.0 |
added 2767 characters in body
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| Jan 19, 2015 at 11:44 | comment | added | Monroe Eskew | Sorry, another question. Can you describe the decoding process more explicitly? It seems like we have to know not just some pair $(C,n)$ to tell us where to concentrate on the $\omega \times \omega_1$ matrix of zeros and ones to see a code for a given $y$, but also a choice of equivalence class representative, what you call $C \setminus B$, and there are more than $\omega_1$ many choices for that. | |
| Jan 19, 2015 at 11:22 | comment | added | Monroe Eskew | Also, how do you go through singulars? Inductively all cardinals $\leq \aleph_\omega$ become countable under your hypothesis, but why $\aleph_{\omega+1}$? | |
| Jan 19, 2015 at 11:16 | comment | added | Monroe Eskew | How do you do the coding using centered ideals? | |
| Jan 19, 2015 at 10:24 | history | answered | Yair Hayut | CC BY-SA 3.0 |