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Post Closed as "Needs details or clarity" by Daniele Tampieri, abx, Max Horn, Carlo Beenakker, domotorp
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YCor
YCor
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Higman's Lemma is basic to WQOlemma and well-quasi-ordering theory, but has many specific forms, for example: the Cartesian product of two wqos is a wqo. Any new extensions?

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 wqoWQO then the finite subsets of Q are wqoWQO by injective order-preserving maps. There could be further Higman (d) and beyond.

Higman's Lemma is basic to 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.

Higman's lemma and well-quasi-ordering theory

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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michael fellows
michael fellows
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Higman's Lemma is basic to 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.