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Keywords:

  • Kripke schema;
  • constructive reverse mathematics;
  • metric space;
  • countable;
  • separable;
  • MSC (2010) 03B30;
  • 03F55;
  • 03F60;
  • 54E35

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.