Supertransitive class

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In set theory, a supertransitive class is a transitive class[1] which includes as a subset the power set of each of its elements.

Formally, let A be a transitive class. Then A is supertransitive if and only if

(∀x)(x∈A→𝒫(x)⊆A).[2]

Here P(x) denotes the power set of x.[3]

See also

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References

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  1. ^ Any element of a transitive set must also be its subset. See Definition 7.1 of Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  2. ^ See Definition 9.8 of Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  3. ^ P(x) must be a set by axiom of power set, since each element x of a class A must be a set (Theorem 4.6 in Takeuti's text above).
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