Timeline for Ramsey Theorem for the class ORD
Current License: CC BY-SA 3.0
11 events
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| Apr 14, 2017 at 23:47 | comment | added | Ali Enayat | @SamDworetzky Your outline is correct (sorry for the tardy reply; I only now saw your question). In the paper with Joel we provide a more direct proof. | |
| Nov 4, 2016 at 19:01 | comment | added | Sam Dworetzky | Thanks for posting the article. Could one also prove this claim in the following way: Suppose for a contradiction that ORD is weakly compact for definable sets in $M\models ZFC$. Then we can build a minimal type $p$ over $M$. Furthermore, $p$ can be used to build a conservative elementary end extension of $M$. However, this is a contradiction since models of ZFC do not have conservative elementary end extensions. | |
| Oct 11, 2016 at 0:27 | comment | added | Joel David Hamkins | I updated with links, now that the article is available. | |
| Oct 11, 2016 at 0:26 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Oct 4, 2016 at 1:51 | history | edited | Andrés E. Caicedo | CC BY-SA 3.0 |
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| Oct 1, 2016 at 13:55 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Oct 1, 2016 at 0:06 | comment | added | Joel David Hamkins | I can agree with that. If you imagine that Ord comes from a large cardinal in some kind of larger universe, then that is precisely what you'd expect. | |
| Sep 30, 2016 at 23:38 | comment | added | Andreas Blass | So in my comment on the question, where I said "Yes, it's true," I should emphasize that I was taking the question very literally, with "definable" applying to the coloring but not to the homogeneous class $H$. | |
| Sep 30, 2016 at 23:36 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Sep 30, 2016 at 23:32 | comment | added | Joel David Hamkins | We can reduce from the $V$-coloring to an Ord-coloring, if we know that there is a definable bijection of $V$ with Ord, but otherwise we seem really to need $V$ rather than Ord in that part. | |
| Sep 30, 2016 at 23:30 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |