[FOM] Query on "Solovay's Inacessible"

[Joe Shipman]

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