Re: Largest Set in ZFC?

Robert E. Beaudoin wrote:
Sure it is, and that's provable in ZF: Let R be the result of iterating the power set operation \omega_1 times, starting from the empty set; R is provably (in ZF) a set. By \epsilon-induction any hereditarily countable set (i.e. any set whose transitive closure is countable) will be an element of R, and so the collection of hereditarily countable sets is a subset of R.

Very good.
Question: does the result still hold if we leave out the wellfoundedness axiom?

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Cheers,
Herman Jurjus
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