sorry, i first lag behind with reading, and then rush with writing before i have read everything that was said. i hope the first paragraph of what i wrote will reawake confusion. it is just a slight variation to what thomas said more precisely. sorry about not reading first :) -- dusko
Have sorted out off line with Jon Sterling what I meant.
I am working in ZFC together wit the axiom that every set is element
of a Grothendieck universe. So I do not use class choice at all but
instead choice in all Grothendieck universes.
What I meant is that one should not reduce choice to the first
universe but instead have it for all sets irrespective of the universe
they live in!
I always found this the most convient setting to work in. But not many
people do it. But if you work in it then there is no need for class
choice anymore.
Sorry for not having expanded my general implicit assumptions beforehand.
I do see that my view is not the majority view.
But it is the most convenient setting for doing category theory in my
eyes and it is weaker than real large cardinal axioms that set theorists
study consider.
Thomas
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