[FOM] Query on "Solovay's Inacessible"

[Ashutosh]

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
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