Timeline for Drawing conclusions by NOT using AC.
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jun 12, 2010 at 20:28 | comment | added | T.. | I think you are referring to Shelah+Woodin, "Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable", Israel J Math 70 (1990) 381-394 showing that $AD_{L(R)}$ follows from supercompact cardinals. How does this relate to provable measurability rather than measurability per se? | |
| Jun 12, 2010 at 19:20 | comment | added | François G. Dorais | Such assumptions, like L(R) satisfies AD, have very high consistency strength. | |
| Jun 12, 2010 at 19:02 | comment | added | T.. | @FGD: +1 ! But are there any results on what constructions do stay inside the provably-measurable world? | |
| Jun 12, 2010 at 18:42 | comment | added | François G. Dorais | It's not true that any construction in ZF + DC is guaranteed to stay within the realm of provably Lebesgue measurable sets. A simple example is a nonmeasurable set in L; the reason why it is measurable in Solovay's model is that every such set is countable in that model. | |
| Jun 12, 2010 at 18:27 | history | answered | T.. | CC BY-SA 2.5 |