Timeline for Partition refinement of a clopen covering in $\Box (\omega+1)^\omega$
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| May 11, 2015 at 12:47 | comment | added | Joel David Hamkins | I think it is fine to keep the question, as long as it is clear what the question is. | |
| May 11, 2015 at 12:44 | comment | added | Dominic van der Zypen | I see... ! Thanks Eric & Joel! - Can Eric write this as an answer, or is it better to delete the question? | |
| May 11, 2015 at 12:40 | comment | added | Joel David Hamkins | Dominic, your edit to the post isn't the same as this! Now Eric's comment seems relevant. | |
| May 11, 2015 at 12:38 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
added 170 characters in body
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| May 11, 2015 at 12:34 | comment | added | Dominic van der Zypen | Exactly, Joel (and let's not forget $f\in V_f$ for $f\in (\omega+1)^\omega$). I will edit the post accordingly | |
| May 11, 2015 at 12:31 | comment | added | Joel David Hamkins | Eric, my understanding of the question is that we want to find clopen $V_f\subset U_f$ with $f\in V_f$ so that $f\neq g\to V_f\cap V_g=\emptyset$. But I see that the OP did not say this exactly. Dominic, could you clarify? | |
| May 11, 2015 at 12:25 | comment | added | Eric Wofsey | Can you not just take the $U_f$'s for $f$ such that if $f(n)<\omega$, then $f(n)<n$? | |
| May 11, 2015 at 12:22 | comment | added | Joel David Hamkins | If the answer is affirmative, then the bounded case is certainly easier; but if the answer is negative, then it may be easier to find a counterexample in the general case. | |
| May 11, 2015 at 12:20 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
added 150 characters in body
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| May 11, 2015 at 12:19 | comment | added | Dominic van der Zypen | Maybe a special case that is more treatable is if I replace $[n,\omega]$ by $[1,\omega]$ in the definition of $U_f$ (or... if that is trivial, $[2, \omega$]). | |
| May 11, 2015 at 12:17 | comment | added | Joel David Hamkins | Dominic, although it is a special case, it isn't clear to me that it is any easier than the general case. | |
| May 11, 2015 at 12:14 | comment | added | Dominic van der Zypen | @JoelDavidHamkins I am asking now for a very particular case of the question you are referring to. Thanks for linking to that question, I will include it in this post. | |
| May 11, 2015 at 12:11 | comment | added | Joel David Hamkins | See the OP's earlier unanswered related question: mathoverflow.net/q/194281/1946. | |
| May 11, 2015 at 12:10 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
better definition of $U_f$
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| May 11, 2015 at 6:31 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |