Talk:Well-quasi-ordering

merge?

Let's have the discussion on the issue of merging at Talk:Well_partial_order PhS 10:32, 5 September 2005 (UTC).

examples

As it stands, the Examples section is not accurately named. IMHO it ought to be called "Examples and Non-Examples" as it also lists (instructive) non-examples. [ɯ:] (talk) 11:54, 30 June 2015 (UTC)

properties

The last item in "Properties of wqos" is probably not what is intended. As it is stated now it is a rather trivial property and the requirement of "upward closedness" is superfluous. The property that is probably intended is that for every downward closed subset $S$ there is a finite subset $M$ such that $x\in S$ if and only if no element $m\in M$ satisfies $m\leq x$.Leen Droogendijk (talk) 12:19, 4 November 2015 (UTC)

formal defintion is too informal

The section formal definition currently states:

Hence a quasi-order ( X {\displaystyle X} X,≤) is wqo if and only if it is well-founded and has no infinite antichains.

Clicking through to well-founded relation states that

a relation is well-founded if it contains no countable infinite descending chains

This suggests that the formal definition is badly worded, or lacking clarity in explaining how and why well-foundedness should be considered as something different from, or needed in addition to the no-anti-chains condition. 67.198.37.17 (talk) 18:13, 2 August 2017 (UTC)

I'm confused. What, more specifically, is wrong with the current definition? Note that the condition of having no infinite descending chain is not the same as the condition of having no infinite antichains. —David Eppstein (talk) 18:26, 2 August 2017 (UTC)