Sentence:  In other words, it is consistent with the axioms[of set theory] to suppose that the <WSD>continuum hypothesis</WSD> is false. (It had been known for some time — see below — that it is consistent with the axioms of set theory to suppose that "CH" is true.) 
Meaning of the word marked with <WSD> tags:  The hypothesis which states that any infinite subset of <big>ℝ</big> must have the cardinality of either the set of natural numbers or of <big>ℝ</big> itself.