The Borel reducibility conjecture for Bratteli diagrams of exact rank

For each $n\geq 1$, let $\mathcal{BD}^*_n$ be the class of Bratteli diagrams of exact rank $n$, and let $BD^*_n$ be the equivalence relation induced by equivalence of Bratteli diagrams on $\mathcal{BD}^*_n$. The exact-rank Bratteli-diagram conjecture. For $n\geq 1$,

$$BD^*_n\leq_B BD^*_{n+1}.$$

Consequently, for $n\geq 3$, $BD^*_n<_B BD^*_{n+1}$. The reverse nonreducibility for $n\geq 3$ is already obtained in the source, but the displayed reducibility was not known there; the conjecture would therefore give strictness in those cases.