Strongly $\eta$-representable degrees and limitwise monotonic functions

It is proved that each strongly $\eta$-representable degree contains a set that is a range of values for some $\boldsymbol0'$-limitwise monotonic function pseudoincreasing on $\mathbb Q$. Thus we obtain a description of strongly $\eta$-representable degrees in terms of $\boldsymbol0'$-limitwise monotonic functions.