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The Kripke schema in metric topology
Author(s) -
Lubarsky Robert,
Richman Fred,
Schuster Peter
Publication year - 2012
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201200018
Subject(s) - mathematics , metric space , separable space , subspace topology , convex metric space , countable set , schema (genetic algorithms) , injective metric space , pure mathematics , discrete mathematics , topology (electrical circuits) , combinatorics , mathematical analysis , computer science , machine learning
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.