**MW:** OK, let’s recap the setup: we have a three-decker ω* ^{U}*⊂

*U*⊂

*V*. So far as

*U*is concerned, ω

*is the “real, true omega”.*

^{U}*V*knows it isn’t. Enayat’s question: what properties must an omega have, for it to be the omega of a model of

*T*? Here

*T*is a recursively axiomatizable extension of ZF, and

*U*is a model of it.