Timeline for Natural combinatorial properties of $\omega_1$ and weakly compact cardinals
Current License: CC BY-SA 3.0
7 events
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| Nov 24, 2016 at 9:54 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 |
added 941 characters in body
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| Nov 24, 2016 at 4:48 | comment | added | Mohammad Golshani | A characterization is given in the paper "Gitik, M.; Magidor, M.; Woodin, H. Two weak consequences of 0♯. J. Symbolic Logic 50 (1985), no. 3, 597–603." but I don't know if it is interesting to you or not. The statement is "There is a club $C$ of $\aleph_1$ consisting of L-inaccessible cardinals such that for each $\alpha$ a limit point of $C, C \cap \alpha$ is almost contained in every closed unbounded subset of $\alpha$ in L". | |
| Nov 23, 2016 at 22:51 | comment | added | Asaf Karagila♦ | I'll edit this tomorrow. I'll sleep on this and see if the morning will bring some better insights as to what are "natural properties" or what aren't. | |
| Nov 23, 2016 at 22:46 | comment | added | user3462 | Yes, I made an edit which was not correct, and deleted it now since you know about it and I was getting into a muddle about it. Perhaps you could mention in your question that such an answer doesn't count? | |
| Nov 23, 2016 at 22:44 | comment | added | Asaf Karagila♦ | (Also, if anything, then the result that MA implies that $\omega_1$ is either computable from a real or weakly compact in L is far more relevant here; that's Theorem C(i) in the linked paper.) | |
| Nov 23, 2016 at 22:40 | comment | added | Asaf Karagila♦ | That is what Mohammad wrote in his now-deleted answer. But I agree that this is not exactly what I was looking for. This is more of a combinatorial property of the continuum, which is definitely not $\omega_1$. But it is an interesting fact, so thank you both for bringing this up. | |
| Nov 23, 2016 at 17:43 | history | asked | Asaf Karagila♦ | CC BY-SA 3.0 |