Similarly, the generalized continuum hypothesis (GCH) states that for every infinite cardinal , there are no cardinals strictly between and . Both the continuum hypothesis and the generalized continuum hypothesis have been proved to be independent of the usual axioms of set theory, the Zermelo–Fraenkel axioms together with the axiom of choice (ZFC).
Similarly the generalized continuum hypothesis (GCH) states that for every infinite cardinal  there are no cardinals strictly between and  Both the continuum hypothesis and the generalized continuum hypothesis have been proved to be independent of the usual axioms of set theory the Zermelo–Fraenkel axioms together with the axiom of choice (ZFC)