[FOM] FROM "Laura Elena Morales Gro." <lemg@matem.unam.mx> Re: WHY DO SET THEORISTS DISLIKE CHRIS FREILING'S EVIDENCE

[Martin Davis]

On Thu, 2 Sep 2004, Timothy Y. Chow wrote:

 > Let me try a less offensive phrasing.  In a world where AC is true, we
 > expect to observe phenomena that violate our intuition about measure.
 >
The axiom cannot be proved or disproved, it's an axiom. In which sense
is it true? Also, there are weird results in mathematics that do not
depend on AC. Constructive decompositions for which the AC is not
necessary. See, for instance, the result by Foreman and Dougherty*
about a finite number of open subsets of the unitary ball in R^n,
disjoint by pairs, which can be grouped in a ball with radius, say,
10^100.

Best regards,
LE

*"Banach-tarski decompositions using sets with the property of Baire", J.
Am. Math. Soc., Vol.7,1 (1994), pp. 75-125.