Timeline for Partition Calculus and Ramsey theory question
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 20, 2019 at 3:02 | comment | added | François G. Dorais | This is definitely the kind of thing I like thinking about. I haven't had any clever ideas yet but you can find my contact info from my website. | |
| Jan 20, 2019 at 2:39 | comment | added | user-1 | If Question 3 is not already known for $n>2$, would you be interested in a collaboration? I answered the $n=2$ case of Question 3, which has given me some idea how one should proceed for the $n>2$ cases. | |
| Jan 20, 2019 at 2:17 | comment | added | François G. Dorais | Rank is much trickier so I'm still thinking about Question 3. Yes, Question 1 does have a positive answer when $\xi$ has countable cofinality. I think you can stretch a Suslin tree to make a counterexample at ordinals of cofinality $\omega_1$. So, if $V=L$, where Suslin trees abound the only positive cases would be at ordinals of countable cofinality and possibly at ordinals of weakly compact cofinality. | |
| Jan 20, 2019 at 2:12 | comment | added | user-1 | I believe Question 1 should have a positive answer for any ordinal of countable cofinality. Your answer suggests that a definitive answer for all $\xi$ is unlikely. You have taken care of Question 2, although the answer is not nearly as nice as I had hoped. I know the answer for the $n=2$ case of Question 3, which is that $\xi$ has this property if and only if it is multiplicatively indecomposable. I had hoped for a similarly nice answer to Question 2. Do you know of any progress on Question 3? | |
| Jan 20, 2019 at 2:06 | vote | accept | user-1 | ||
| Jan 20, 2019 at 1:56 | history | edited | François G. Dorais | CC BY-SA 4.0 |
outline of weakly compact case
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| Jan 20, 2019 at 1:50 | history | edited | François G. Dorais | CC BY-SA 4.0 |
outline of weakly compact case
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| Jan 20, 2019 at 1:37 | history | answered | François G. Dorais | CC BY-SA 4.0 |