Timeline for Sets of Vitali's type in models of $\mathsf{ZF}+\mathsf{GCH}$ where $V \neq L$
Current License: CC BY-SA 3.0
4 events
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Dec 30, 2014 at 15:56 | comment | added | Thomas Benjamin | Actually, I should really say that evolving mathematical practice might force one to construct a new Vitali set not in $L$--sorry. As for the 'evolving continuum' one could always form new Vitali sets by adding reals so as not to violate CH, right? | |
Dec 30, 2014 at 15:34 | comment | added | Thomas Benjamin | @Prof. Hamkins: Thank you for that very nice answer--it is very helpful. The case that interests me most is the last one, that is, the case where one forces to add a new Vitali set without adding reals so that one can have $ZFC+GCH$+$V$$\neq$$L$ with Vitali sets in both $L$ and $V-L$. In this case, is there a way to distinguish the Vitali sets in $L$ from those in $V-L$? I ask this question to see if it makes sense to speak of an 'evolving continuum'--that is, a continuum that grows larger to meet the needs of evolving mathematical practice. | |
Dec 30, 2014 at 15:18 | vote | accept | Thomas Benjamin | ||
Dec 30, 2014 at 14:24 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |