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

[axiom for a new set from any given set]

5 ideas
Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
Powers: All the subsets of a given set form their own new powerset [Clegg]
The Power Set is just the collection of functions from one collection to another [Lavine]
If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt]