Single Idea 13037

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V]

Full Idea

Axiom of Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x). That is, there is a set which contains zero and all of its successors, hence all the natural numbers. The principal of induction rests on this axiom.

Gist of Idea

Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x)


Kenneth Kunen (Set Theory [1980], 1.7)

Book Reference

Kunen,Kenneth: 'Set Theory: Introduction to Independence Proofs' [North-Holland 1980], p.19

Related Idea

Idea 15931 The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine]