The Kripke schema in metric topology
Robert S. Lubarsky, Fred Richman, Peter M. Schuster · Mathematical logic quarterly · 2012
Abstract A form of Kripke's schema turns out to be equivalent to each of the following two statements from metric topology: every open subspace of a separable metric space is separable; every open subset of a separable metric space is a countable union of open balls. Thus Kripke's schema serves as a point of reference for classifying theorems of classical mathematics within Bishop‐style constructive reverse mathematics.