[FOM] Query on "Solovay's Inacessible"
JoeShipman at aol.com
Sun Apr 28 08:06:05 EDT 2013
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?
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