I think you mean to say is “non-Well-founded sets exist!” since you are talking about the antifoundational case (and even with strong anti-foundation axioms I still have well-founded sets to play with also).
Oops. Fixed.
I think you mean to say is “non-Well-founded sets exist!” since you are talking about the antifoundational case (and even with strong anti-foundation axioms I still have well-founded sets to play with also).
Oops. Fixed.