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feat(set_theory/zfc/ordinal): definition of von Neumann ordinals#18513
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feat(set_theory/zfc/ordinal): definition of von Neumann ordinals#18513
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Could the @vihdzp and @negiizhao work out which of these two PRs should remain open, and close the other one? |
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The other PR was closed. |
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| - A transitive set that's (strictly) totally ordered under `∈`. | ||
| - A transitive set that's well-ordered under `∈`. | ||
| -/ | ||
| def is_ordinal (x : Set) : Prop := x.is_transitive ∧ ∀ y z w : Set, y ∈ z → z ∈ w → w ∈ x → y ∈ w |
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| def is_ordinal (x : Set) : Prop := x.is_transitive ∧ ∀ y z w : Set, y ∈ z → z ∈ w → w ∈ x → y ∈ w | |
| def is_ordinal (x : Set) : Prop := x.is_transitive ∧ ∀ w ∈ x, w.is_transitive |
the definition here is just writing out what is_transitive means, which seems unnecessary.
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We define von Neumann ordinals and prove some very basic theorems.
For the reasoning behind my choice of definition, see https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/hereditarily/near/338586303.