  A set of integers $A$ is computably encodable if every infinite set of
integers has an infinite subset computing $A$. By a result of Solovay, the
computably encodable sets are exactly the hyperarithmetic ones. In this paper,
we extend this notion of computable encodability to subsets of the Baire space
and we characterize the $\Pi^0_1$ encodable compact sets as those who admit a
non-empty $\Sigma^1_1$ subset. Thanks to this equivalence, we prove that weak
weak K\"onig's lemma is not strongly computably reducible to Ramsey's theorem.
This answers a question of Hirschfeldt and Jockusch.
