 Harvey Friedman has established the following theorem: roughly, if \(S\) is a Borel set, then there exists a Borel function \(f\) such that the graph of \(f\) is either included in or disjoint from \(S\). Friedman showed that this simple-sounding theorem is not provable even in full second-order arithmetic P\(^2\), but proving it necessarily requires the full power of ZFC (see Simpson 1999: 23).