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Wetzel: Formalisation of an Undecidable Problem Linked to the Continuum Hypothesis (2205.03159v2)
Published 6 May 2022 in cs.LO
Abstract: In 1964, Paul Erd\H{o}s published a paper settling a question about function spaces that he had seen in a problem book. Erd\H{o}s 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 integrates set theory with higher-order logic.