As noted in the previous paragraph, second-order comprehension axioms easily generalize to the higher-order framework. However, theorems expressing the "compactness" of basic spaces behave quite differently in second- and higher-order arithmetic: on one hand, when restricted to countable covers/the language of second-order arithmetic, the compactness of the unit interval is provable in WKL0 from the next section. On the other hand, given uncountable covers/the language of higher-order arithmetic, the compactness of the unit interval is only provable from (full) second-order arithmetic (). Other covering lemmas (e.g. due to Lindelöf, Vitali, Besicovitch, etc.) exhibit the same behavior, and many basic properties of the gauge integral are equivalent to the compactness of the underlying space.