Remark on my paper: On Skolem's theorem.
Gaisi Takeuti · Journal of the Mathematical Society of Japan · 1957
It was proved in my paper [1] that if the system of axioms of Fraenkel-von Neumann of the set-theory is consistent, then system remains consistent after addition of the axiom that every set is a univalent image of $\omega$ .This result was established by Theorems 1,2