# Abstract [Mathscinet review](https://mathscinet.ams.org/mathscinet/article?mr=39778) For every $\alpha<\omega_\mu$, let $M_\alpha$ denote a set of sequences of type $\alpha$ composed of zeros and ones, and suppose that, for every pair of ordinal numbers $\alpha$ and $\beta$ with $\alpha<\beta<\omega_\mu, M_\alpha$ is the set of segments of type $\alpha$ of the sequences of $M_\beta$. The problem in question is: Is there necessarily a set $M$ of sequences of type $\omega_\mu$ such that every $M_\alpha, \alpha<\omega_\mu$, is the set of segments of type $\alpha$ of the sequences of $M$ ? Let $\gamma=c f\left(\omega_\mu\right)$. The answer is affirmative if $\gamma=0$, negative if $\gamma$ is an isolated number, and the problem is open if $\gamma$ is a transfinite limit number.