 Zermelo’s axiomatization of set theory (1908; for more details see entries on  set theory,  the early development of set theory,  alternative axiomatic set theories)  supplied a sensible tool for blocking contradictions. The main ideas of the axiomatization can be summarized as follows: (i) naïve comprehension is restricted to a separation axiom, i.e., to a principle granting the existence of enough subsets of an already given set of objects (numbers, points, functions on a given space); ‘enough subsets’ here refers to all the subsets specifiable by means of definite conditions involving the primitive notions (set equality and membership) and satisfying the laws of classical logic; (ii) there are axioms ensuring that the basic operations of forming singleton, union, pairing, and power set are well defined and that there exist at least an infinite set and the empty set; (iii) extensionality is assumed: two sets are equal if and only if they have the same elements; (iv) an axiom of choice is postulated, which allows selecting a choice set out of any family of disjoint non-empty sets.