= Solution
Take the <first-order theory> of an <infinite set> in the <first-order language> of <logical equality> alone, with an axiom asserting at least $n$ distinct elements for each positive <integer> $n$. It is complete and eliminates <quantifiers>: a new <logical variable> either equals a specified old <logical variable> or is required to avoid only finitely many existing values, which an infinite domain permits.
For every infinite cardinal $\kappa$, any two <first-order models> of size $\kappa$ are <isomorphic> because every <bijection> between their underlying <sets> preserves <logical equality>, the whole <first-order language>. Thus
$$
\boxed{T_{\infty}\text{ is categorical in every infinite cardinality}.}
$$
Its complete $n$-types record only the partition of coordinate indices according to <logical equality>. There are finitely many such partitions, and each is isolated by the corresponding <logical equalities> and inequalities. Ryll-Nardzewski therefore recovers <countable> categoricity; there are no nonprincipal complete finite-arity <partial types> to omit in this example.
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