# Abstract [Mathscinet review](https://mathscinet.ams.org/mathscinet/article?mr=39779) 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 $M$ ? The problem with the additional hypothesis that the cardinal number of $M_\alpha$ is less than $\aleph_\mu$ for every $\alpha<\omega_\mu$. Inspired by [[Helson - On a problem of Sikorski|Helson]]'s method, the author shows that the answer is negative for $\mu=1$. Sikorski and the author observe that, under the generalized hypothesis of the continuum, the answer is negative for $\mu=\nu+1$ if $\omega_\nu$ is a regular initial number.