Timeline for Proofs that require fundamentally new ways of thinking
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 3, 2017 at 20:03 | comment | added | FNH | @ChadGroft, Could you please clarify that more or refer to some papers/articles explaing/motivating forcing from this view? | |
| Feb 15, 2014 at 7:53 | comment | added | Stefan Geschke | I don't agree with Chad Croft that "generic filters fall right out". I believe that Boolean valued models are natural and also using ultrafilters in order to turn them into 2-valued models, but using generic filters to get actual ZFC models is on a different level. Also, the use of partial orders instead of Boolean algebras seems slightly unintuitive, even though it is more practical. | |
| Feb 15, 2014 at 7:43 | history | edited | Stefan Geschke | CC BY-SA 3.0 |
Changed "independent results" to "independence results"
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| Dec 14, 2010 at 2:48 | comment | added | Andrés E. Caicedo | @Chad : Very interesting! Curious that his description is so "recursion-theoretic." Do you remember when was this course? | |
| Dec 14, 2010 at 2:07 | comment | added | Chad Groft | I took the last set theory course that Cohen taught, and this isn't how he presented his insight at all (though his book takes this approach). The central problem is "how do I prove that non-constructible [sub]sets [of N] are possible without access to one?", and his solution is "don't use a set; use an adaptive oracle". Once that idea is present, the general method falls right into place. The oracle's set of states can be any partial order, generic filters fall right out, names are clearly necessary, everything else is technical. The hardest part is believing it will actually work. | |
| Dec 9, 2010 at 16:52 | history | answered | Andrés E. Caicedo | CC BY-SA 2.5 |