[FOM] Query on "Solovay's Inacessible"

Ashutosh ashu1559 at gmail.com
Sun Apr 28 19:01:47 EDT 2013


Yes. This is because, in the theory ZF + DC, one can show that either
omega_1 is inaccessible in L or there is a Sigma-1-3 Lebesgue non
measurable set of reals. This is due to Shelah.

Ashutosh


On Sun, Apr 28, 2013 at 7:06 AM, Joe Shipman <JoeShipman at aol.com> wrote:

> According to Solovay and Shelah,
>
> Con(ZFC + Inacc) <--> Con(ZF + DC + "All sets of reals are Lebesgue
> measurable")
>
> I wonder how much further this equivalence can be pushed. From (ZFC +
> Inacc) one can prove Con(ZF);  does the axiom system (ZF + DC + "All sets
> of reals are Lebesgue measurable") also prove Con(ZF), or any other
> arithmetical sentence that is not a consequence of ZF?
>
> -- JS
>
>
> Sent from my iPhone
> _______________________________________________
> FOM mailing list
> FOM at cs.nyu.edu
> http://www.cs.nyu.edu/mailman/listinfo/fom
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20130428/0f2f82c3/attachment.html>


More information about the FOM mailing list