Wetzel: Formalisation of an Undecidable Problem Linked to the Continuum Hypothesis

Abstract

In 1964, Paul Erdős published a paper [5] settling a question about function spaces that he had seen in a problem book. Erdős proved that the answer was yes if and only if the continuum hypothesis was false: an innocent-looking question turned out to be undecidable in the axioms of ZFC. The formalisation of these proofs in Isabelle/HOL demonstrate the combined use of complex analysis and set theory, and in particular how the Isabelle/HOL library for ZFC [16] integrates set theory with higher-order logic.