feat(set_theory/zfc/ordinal): definition of von Neumann ordinals #18513
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
vihdzp
added
the
awaiting-review
4 tasks
1 task
1 task
|
Could the @vihdzp and @negiizhao work out which of these two PRs should remain open, and close the other one? |
semorrison
added
awaiting-author
|
The other PR was closed. |
vihdzp
added
awaiting-review
eric-wieser
added
the
not-too-late
digama0
reviewed
Jul 26, 2023
| - 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 |
There was a problem hiding this comment.
Suggested change
| 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.
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
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.