= Solution
The same <complete theory> $T_\infty$ of an infinite pure <set> provides this property directly. For $n$ <logical variables>, each <complete type> specifies exactly which <logical variables> are equal. <First-order consistency> requires an <equivalence relation> on the finite index <set>, and infinitude ensures every such partition is realizable. Hence
$$
\boxed{|S_n(T_\infty)|=B_n<\infty,}
$$
where $B_n$ is the $n$th <Bell number>, counting partitions of an $n$-element <set>. For example the first values are $B_1=1$, $B_2=2$ and $B_3=5$. The isolating <conjunction> lists <logical equality> within blocks and inequality between blocks. This explicitly verifies the hypothesis which Ryll-Nardzewski identifies with $\aleph_0$-categoricity.
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