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• CommentRowNumber1.
• CommentAuthorTodd_Trimble
• CommentTimeSep 8th 2012

I made some edits at well-order. I am removing a query box, having duly extracted some punchlines. These edits also forced an edit to partial function, where I added the generalization to partial maps in any category with pullbacks.

+– {: .query} This need not exist; in particular, $S_a$ may be empty. What do we really want to say here? (We could talk about the successor of a well-ordered set.) —Toby Mike: Yeah, or we could say that successor is a partial function. One definition of a limit ordinal is one on which successor is totally defined. =–

• CommentRowNumber2.
• CommentAuthorTobyBartels
• CommentTimeSep 9th 2012

Good; I added redirects such as partial map.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 23rd 2017

At well-order I found it non-trivial to extract the usual classical definition. (Before I reached the second-but-last bullet item that states it, I was following a dozen links to other kinds of orderings and their properties).

For the sake of the reader, I have now given the usual definiton the first paragraph in the Definition section (I didn’t remove it from that bullet list).

But I think some expert might still make that entry a bit user-friendly.

• CommentRowNumber4.
• CommentAuthorDavidRoberts
• CommentTimeMay 24th 2017

I linked well-order and well-quasi-order. I do wonder whether there are constructions that assume an index set needs to be well-ordered that could use the weaker notion. I don’t know the consistency of asking that every set admits a well-quasi-order, but surely it’s weaker than full AC.