[FOM] "Mathematician in the street" on AC

Ashutosh ashu1559 at gmail.com
Wed Sep 2 18:59:35 EDT 2009

On Mon, Aug 31, 2009 at 3:41 PM, Vaughan Pratt <pratt at cs.stanford.edu> wrote:

> (As an aside, is the Solovay result that every set could be Lebesgue-measurable consistent with the Feferman-Levy result that the reals could be a countable union of countable sets?  I don't right away see how either possibility implies the negation of the other.)

They used different models. In Solovay's model the axiom of dependent
choice, which implies countable choice, holds - this suffices to prove
that countable union of null sets is null. Needless to say, in Levy's
model, this doesn't hold.


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