  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.
