More conservativity for weak Kőnig's lemma

We prove conservativity results for weak Kőnig’s lemma that extend the celebrated result of Harrington (for ${\mathrm{\Pi }}_1^1$-statements) and are somewhat orthogonal to the extension by Simpson, Tanaka and Yamazaki (for statements of the form $\mathrm{\forall }X\mathrm{\exists }!Y\psi$ with arithmetical $\psi$). In particular, we show that ${\mathsf{W}\mathsf{K}\mathsf{L}}_0$ is conservative over ${\mathsf{R}\mathsf{C}\mathsf{A}}_0$ for well-ordering principles. We also show that compactness (which characterizes weak Kőnig’s lemma) is dispensable for certain results about continuous functions with isolated singularities.