Single Idea 13038

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI]

Full Idea

Power Set Axiom: ∀x ∃y ∀z(z ⊂ x → z ∈ y). That is, there is a set y which contains all of the subsets of a given set. Hence we define P(x) = {z : z ⊂ x}.

Gist of Idea

Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y)

Source

Kenneth Kunen (Set Theory [1980], §1.10)

Book Reference

Kunen,Kenneth: 'Set Theory: Introduction to Independence Proofs' [North-Holland 1980], p.29

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