  In general, the (known) sentences of set theory are either like CH or PM.  Some are like CH in that both ZFC+φ and ZFC+ ¬φ lie in the degree of ZFC.  Others are like PM in that one of ZFC+φ and ZFC+ ¬φ lies in the degree of ZFC while the other lies in the degree of an extension of ZFC via a large cardinal axiom.