Definition:Zermelo Set Theory/Historical Note

Historical Note on Zermelo Set Theory
The axiomatic system of Zermelo Set Theory was created by as way to circumvent the logical inconsistencies of Frege set theory.

The  was derived from the axiom of abstraction, with a domain strictly limited to the elements of a given pre-existing set.

Further axioms were then developed in order to allow the creation of such pre-existing sets:
 * the, allowing for the existence of $\O := \set {}$
 * the, allowing for $\set {a, b}$ given the existence of $a$ and $b$
 * the, allowing for $\bigcup a$ given the existence of a set $a$ of sets
 * the, allowing for the power set $\powerset a$ to be generated for any set $a$
 * the, allowing for the creation of the set of natural numbers $\N$.