  In the paper "Randomizations of Scattered Sentences", Keisler showed that if
Martin's axiom for aleph one holds, then every scattered sentence has few
separable randomizations, and asked whether the conclusion could be proved in
ZFC alone. We show here that the answer is "yes". It follows that the absolute
Vaught conjecture holds if and only if every $L_{\omega_1\omega}$-sentence with
few separable randomizations has countably many countable models.
