Timeline for singularize the least inaccessible?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| S Jan 28, 2015 at 20:50 | history | suggested | Ed Dean |
added [lo.logic] tag
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| Jan 28, 2015 at 20:41 | review | Suggested edits | |||
| S Jan 28, 2015 at 20:50 | |||||
| Jan 28, 2015 at 14:57 | vote | accept | Monroe Eskew | ||
| Jan 28, 2015 at 14:20 | answer | added | Yair Hayut | timeline score: 11 | |
| Jan 28, 2015 at 13:23 | comment | added | Joel David Hamkins | @YairHayut Please post an answer giving this argument. | |
| Jan 28, 2015 at 13:07 | comment | added | Yair Hayut | Joel is right, is it consistent relative to a measurable. You can use the paper of Magidor and Vaananen "On Lowenheim-Skolem-Tarski number for extension of first order logic", where, in the model that they construct, the first inaccessible can change its cofinality to $\omega$ without adding bounded sets or collapsing cardinals. In this paper, they use supercompact in order to get some strong reflection properties. If we don't want those reflection properties, it can be done also from one measurable. | |
| Jan 28, 2015 at 13:00 | comment | added | Joel David Hamkins | Very nice question. You will need a measurable cardinal, since the tail filter on the singularizing sequence will construct an inner model with a measurable cardinal. But if $\kappa$ is measurable (and the GCH holds), then you can make it the least inaccessible and then try to use the ground model Prikry forcing. Does this preserve cardinals? I need to think a little more about it. | |
| Jan 28, 2015 at 12:47 | history | asked | Monroe Eskew | CC BY-SA 3.0 |