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This tag is for questions about proving that some statement is independent from a theory, meaning it is neither provable nor refutable from that theory. Common examples are the continuum hypothesis from the axioms of ZFC, and the axiom of choice from the axioms of ZF.

6 votes

What are some reasonable-sounding statements that are independent of ZFC?

"There exists a complete metric space $(X,d)$ and a Borel probability measure $\mu$ on $X$ with non-separable support." This has been discussed elsewhere on MO (I forget where, sorry), but is shown to …