[FOM] Query on "Solovay's Inacessible"

Andres Caicedo caicedo at diamond.boisestate.edu
Sun Apr 28 18:15:10 EDT 2013

Yes, of course. The theory ZF+DC+Lebesgue measurability implies that 
omega_1 is inaccessible in L. This shows that the theory proves that there 
is a standard model of ZFC and much more.


On Sun, 28 Apr 2013, Joe Shipman 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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