Timeline for Consistency of: "The continuum function is injective, and for all infinite cardinals $\kappa$ we have that $2^\kappa$ is weakly inaccessible."
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 11, 2014 at 3:56 | vote | accept | goblin GONE | ||
| May 10, 2014 at 4:52 | comment | added | Mohammad Golshani | I don't know inner model theory, but I think the statement, if consistent, needs much larger cardinals. I think we even need a proper class of cardinals $\kappa$ of Mitchell order an inaccessible above $\kappa$, and even more. | |
| May 9, 2014 at 12:39 | vote | accept | goblin GONE | ||
| May 9, 2014 at 12:39 | |||||
| May 8, 2014 at 17:58 | comment | added | Noah Schweber | (cont'd) See e.g. cantorsattic.info/Mitchell_rank for a definition of Mitchell order. Basically, Gitik's assumption is that there is a measurable cardinal which admits as big measures as possible. | |
| May 8, 2014 at 17:54 | comment | added | Noah Schweber | Expanding on Joel's last paragraph: in 1991, building off a long chain of results, Moti Gitik showed (ac.els-cdn.com/016800729190016F/…; see also download.springer.com/static/pdf/968/…, page 247) that $ZFC+\neg SCH$ is equiconsistent with $ZFC+$"There is a measurable cardinal $\kappa$ of Mitchell order $\kappa^{++}$." | |
| May 8, 2014 at 16:13 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| May 8, 2014 at 16:03 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |