[FOM] Re: L-measurable sets

Kanovei kanovei at wmwap1.math.uni-wuppertal.de
Sun Jul 20 23:29:18 EDT 2003

From: "Ali Enayat" <enayat at american.edu>
To: <fom at cs.nyu.edu>
Date: Sun, 20 Jul 2003 22:01:03 -0400
Corollary: If M is an inner model of a model M' of ZFC, then the
reals of M are either (A) of measure 0, or (B) not measurable.

Question: Clearly (A) in the corollary above can be arranged by forcing the
continuum of M to become countable in a generic extension M[G]=M'.  What
about (B)?

Adding any number of random reals to M, we obtain a model 
where M\cap R is not Lebesgue measurable (and continuum as 
large as desired). 


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