Swelled Set which is Closed under Chain Unions with Choice Function is Type M/Historical Note

Historical Note on Swelled Set which is Closed under Chain Unions with Choice Function is Type $M$

Smullyan and Fitting, in their Set Theory and the Continuum Problem, revised ed. of $2010$, demonstrate only the sufficient condition: that a swelled set with the given criteria is of type $M$.

In raising the question as to whether such a set of sets which is not swelled would also be of type $M$, they say:

We posed this question to Professor Herman Rubin, who informed us that it would not.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text {II}$ -- Maximal principles: $\S 6$ Another approach to maximal principles