The Continuum Hypothesis is independent of ZFC, the standard axiomatic system used as a foundation for mathematics, meaning that it can neither be proven nor disproven from the axioms. However, it's possible that mathematicians will accept new axioms into the framework eventually, which could decide the truth value of CH.

This market resolves if the Continuum Hypothesis is ever proven or disproven in an axiomatic system accepted by the overwhelming majority of mathematicians (the way ZFC is now), or an extension of such a system that only adds axioms saying that the system is consist (e.g., ZFC+Con(ZFC), where Con(X) is shorthand for an axiom stating that the formal system X is consistent). Adding multiple consistency axioms is acceptable as well, e.g. ZFC+Con(ZFC)+Con(ZFC+Con(ZFC)), or even ZFC+"∀n∈ℕ Con(ZFC_n)", where ZFC_0=ZFC and ZFC_(n+1)=ZFC_n+Con(ZFC_n) (and of course, you could go even further with this using transfinite ordinals).