Timeline for A question about "local" versus "global" large cardinal axioms
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 16, 2014 at 19:30 | vote | accept | Garabed Gulbenkian | ||
| S Jun 16, 2014 at 12:04 | history | suggested | F. C. |
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| Jun 16, 2014 at 12:00 | review | Suggested edits | |||
| S Jun 16, 2014 at 12:04 | |||||
| Jun 15, 2014 at 19:38 | answer | added | Joel David Hamkins | timeline score: 12 | |
| Jun 15, 2014 at 19:06 | comment | added | Monroe Eskew | @NoahS To answer your question about least Woodin, Magidor proved from Con(ZFC+supercompact) that there can be a supercompact with no strong compacts below. But supercompact is always a limit of Woodins. | |
| Jun 15, 2014 at 18:59 | comment | added | Noah Schweber | At the same time, I think the global/local distinction might be misleading: measurability sounds like a local definition, but maybe the "right" way to think of it is as providing a global object. | |
| Jun 15, 2014 at 18:58 | comment | added | Noah Schweber | Not related to your more specific question, but maybe still interesting: the existence of a strongly compact cardinal has strictly greater consistency strength than the existence of a Woodin cardinal; and in my view, the first is "local" and the second is "global." Of course, the relevant question is whether the least Woodin can be smaller than the least strongly comapct, which I don't know the answer to. | |
| Jun 15, 2014 at 18:58 | comment | added | Monroe Eskew | You'd have to have a "local" axiom which is nonetheless more complex than usual, namely more than $\Sigma_2$. | |
| Jun 15, 2014 at 18:43 | history | asked | Garabed Gulbenkian | CC BY-SA 3.0 |