Definition:Inductive Set/Axiomatic Set Theory

Definition

The concept of an inductive set is axiomatised in the Axiom of Infinity in Zermelo-Fraenkel set theory:

$\exists x: \paren {\paren {\exists y: y \in x \land \forall z: \neg \paren {z \in y} } \land \forall u: u \in x \implies \paren {u \cup \set u \in x} }$

Sources

• 1960: Paul R. Halmos: Naive Set Theory ... (previous) ... (next): $\S 11$: Numbers