More conservativity for weak K\H{o}nig's lemma

TL;DR

This paper extends conservativity results for weak K\

Contribution

It proves new conservativity results for weak K\

Findings

WKL\

WKL\

Compactness is dispensable for some results about continuous functions with isolated singularities.

Abstract

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