Editing Kripke–Platek set theory (section)

=== Empty set ===
If any set <math>c</math> is postulated to exist, such as in the axiom of infinity, then the axiom of empty set is redundant because it is equal to the subset <math>\{x\in c\mid x\neq x\}</math>. Furthermore, the existence of a member in the universe of discourse, i.e., ∃x(x=x), is implied in certain formulations<ref>{{cite book |title=A course in model theory: an introduction to contemporary mathematical logic |url=https://archive.org/details/courseinmodelthe0000poiz |url-access=registration |last=Poizat |first=Bruno |year=2000 |publisher=Springer |isbn=0-387-98655-3}}, note at end of §2.3 on page 27: "Those who do not allow relations on an empty universe consider (∃x)x=x and its consequences as theses; we, however, do not share this abhorrence, with so little logical ground, of a vacuum."</ref> of [[first-order logic]], in which case the axiom of empty set follows from the axiom of Δ<sub>0</sub>-separation, and is thus redundant.