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Higman's Lemma is basic to well-quasi-ordering (WQO) theory, but has many specific forms, for example: the Cartesian product of two WQOs is a WQO. Any new extensions?

Usually proved by minimal bad sequence arguments. Besides Cartesian product Higman (a), There is Higman (b) re injective order-preserving finite subsequences, and Higman (c) which says that if Q is a WQO then the finite subsets of Q are WQO by injective order-preserving maps. There could be further Higman (d) and beyond.

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  • $\begingroup$ What is a "WQO"? I think it would help your question if you expanded everything a bit and explained what is what. Also, it is not really clear to me what you are asking. $\endgroup$
    – Max Horn
    Commented Nov 27, 2023 at 9:04
  • $\begingroup$ en.wikipedia.org/wiki/Well-quasi-ordering $\endgroup$
    – Emil Jeřábek
    Commented Nov 27, 2023 at 9:06
  • $\begingroup$ Please ask again this question in a clearer form. $\endgroup$
    – domotorp
    Commented Nov 28, 2023 at 5:16

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