Titlebook: Well-Quasi Orders in Computation, Logic, Language and Reasoning; A Unifying Concept o Peter M. Schuster,Monika Seisenberger,Andreas Weie Bo

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Book 2020highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept fo

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Well Quasi-orderings and Roots of Polynomials in a Hahn Field, a polynomial, in terms of the lengths of the coefficients [., .]. In the present paper, we give an introduction to Hahn fields, we indicate how well quasi-orderings arise when we try to bound the lengths of sums and products, and we re-work, in a more general way, a technical theorem from [.] that gives information on the root-taking process.

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Well Quasi-orders and the Functional Interpretation,der problems which are related to this, particularly the question of the constructive meaning of Zorn’s lemma and the notion of recursion over the non-wellfounded lexicographic ordering on infinite sequences.

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,Well-Partial Orderings and their Maximal Order Types,-product and an application of de Jongh and Parikh’s work, we give new and easier proofs of Higman’s, Kruskal’s and Nash–Williams’ theorems that the partial orderings considered are indeed w.p.o.’s. We also apply our results to the theory of ordinal notations.

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