Timeline for Ground Axiom and behaviors of continuum function
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 10, 2014 at 17:30 | comment | added | user47697 | I think it is a really interesting subject to follow. | |
| Mar 10, 2014 at 17:12 | comment | added | Joel David Hamkins | I don't know of any inconsistencies between GA and the values of the continuum, and the argument I mentioned in my answer suggests that one can get GA with any Easton function on the regular cardinals (but as I said one should still check all the details). | |
| Mar 10, 2014 at 17:09 | vote | accept | CommunityBot | ||
| Mar 10, 2014 at 17:03 | comment | added | user47697 | So is it true to say the Ground Axiom doesn't carry any information about the behavior of continuum function or there are some (few) known inconsistencies between some non-trivial values of continuum function and $GA$? | |
| Mar 10, 2014 at 16:34 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Mar 10, 2014 at 16:23 | comment | added | Joel David Hamkins | An interesting tidbit: the authors of that paper constitute three mathematical generations, since the third author was the Ph.D. supervisor of the first, who was the Ph.D. supervisor of the second. | |
| Mar 10, 2014 at 16:16 | comment | added | Nate Eldredge | Ok, so you just had a typo (which I see you've fixed). Thanks for the clarification! | |
| Mar 10, 2014 at 16:15 | comment | added | Joel David Hamkins | Sorry, I fixed the typo (thanks!). The linked paper proves the consistency with V$\neq$HOD. The consistency of GA with V=HOD was already known in the dissertation of Jonas Reitz, who proved that GA is a consequence of the Continuum Coding Axiom, which is a strong version of V=HOD. We didn't at that time know how to force GA except by this strong coding method, and the paper with Woodin solved that problem by providing an alternative way to prove GA. The end result is that almost any class length iteration of progressively closed forcing will force GA. | |
| Mar 10, 2014 at 16:13 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Mar 10, 2014 at 16:07 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |