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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 Ref
Kunen,Kenneth: 'Set Theory: Introduction to Independence Proofs' [North-Holland 1980], p.29
13038 | Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt] |