Re: The set-theoretic platinum standard


Herman Rubin wrote:
In article <1151786351.970611.215510@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Gene Ward Smith <genewardsmith@xxxxxxxxx> wrote:

How about the Banach-Mazur paradox? An alternative axiom,
the Axiom of Determinateness, has been proposed to resolve
this. It does give dependent choice, which is adequate for
most of analysis, at least.

It's not a paradox, and AD is intuitively false in my opinion. My
reasoning here is the
Puree Intution, which says you can take the numbers between 0 and 1, or
just the irrational numbers between 0 and 1, put your conceptual
blender on puree, and evenly mix together two sets of size the
continuum. If one set is the red set, and the other set is the green
set, you put your blender on puree, and you get an even yellow. No
matter how much you magnify, you still get even yellow. Hence playing a
Banach-Mazur game, we don't have a strategy for either side, because no
regions are any more or any less green than any other regions.

.

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