Re: Largest Set in ZFC?

On 2008-03-15, in sci.logic, Robert E. Beaudoin wrote:
I seem to recall that absent foundation one can have a proper class
of solutions to x = {x} (consistently with the rest of ZF), each of
which would be hereditarily countable.

It's consistent with ZFC with ur-elements that the ur-elements form a
proper class. Pick a model of this theory and replace each ur-element
with a set having itself as the sole member and you'll get a model of
ZFC without foundation and with a proper class of solutions to x =
{x}.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

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

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