[FOM] Concerning Probability Measures

[Harvey Friedman]

I have a recollection that there is an old result of Solovay that is
relevant to the discussion with Shipman about RVM. It is a result about ZF
without choice (say with dependent choice):

ZFDC + "there is a countably additive probability measure on all subsets of
[0,1]"

and 

ZF

are equiconsistent (in fact, mutually interpretable).

Correct me if I am wrong. (Adding omega_2 random reals and taking L(R)?).

This means that the great strength of "there is a ... " is dependent on
having the axiom of choice.

Harvey Friedman