If ZFC is consistent, then it cannot prove the existence of a model of ZFC, for otherwise ZFC would prove its own consistency. Thus, a proof of consistency or of undecidability of a given sentence \(\varphi\) is always a relative consistency proof. That is, one assumes that ZFC is consistent, hence it has a model, and then one constructs another model of ZFC where the sentence \(\varphi\) is true. We shall see several examples in the next sections.