Re: Choice and ur-elements

On 2007-04-27, zuhair wrote:
What is the relationship between choice and existence of ur-elements?

Both choice and failure of choice are compatible with existence of
ur-elements, as well as with non-existence of ur-elements.

I ask this question because I read that before Cohen proved the
independence of choice from other axioms of ZFC, it was a must that
any set theory should be able to be modified such as to include ur-
elements, but after Cohen proved the independence of choice from other
axioms of ZFC, it is no longer demanded that a set theory should allow
for such modification.

Where did you read this? Perhaps what you read was a reference to a proof of
independence of choice in presence of ur-elements, using so-called
Fraenkel-Mostowski permutation models.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

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