The four central axioms of Zermelo's system are the Axioms of Infinity and Power Set, which together show the existence of uncountable sets, the Axiom of Choice, to which we will devote some space below, and the Axiom of Separation. This latter allows that any ‘definite’ property φ does in fact give rise to a set, namely the set of all those things which are already included in some set a and which have the property φ, in other words, gives rise to a certain subset of a, namely the subset of all the φ-things in a. Thus, it follows from this latter that there will generally be many sets giving partial extensions of φ, namely the φ-things in a, the φ-things in b, the φ-things in c, and so on. However, there will be no guarantee of the existence of a unique extension-set for φ, as, of course, there is under the CP, namely a = {x : φ(x)}.