Within the framework of Zermelo–Fraenkel set theory, the axiom of power set guarantees the existence of the power set of any given set. Furthermore, the axiom of infinity guarantees the existence of at least one infinite set, namely a set containing the natural numbers. There are alternative set theories, e.g. "general set theory" (GST), Kripke–Platek set theory, and pocket set theory (PST), that deliberately omit the axiom of power set and the axiom of infinity and do not allow the definition of the infinite hierarchy of infinites proposed by Cantor.