Abstract
A well ordering has the property that any non-empty subset has a minimum element. In [Girard
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(i)
ATR0 proves that the collection S n of countable scattered linear orderings at level n of the Hausdorff hierarchy is better quasi ordered (bqo), and
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(ii)
ATR0 proves that "if α is an ordinal and Q is bqo then Q α is bqo".
We conjecture that the techniques introduced will eventually allow a proof in ATR0 of Fraïssé's order type conjecture (proved by R. Laver) which states that the collection L of all countable linear orderings is wqo under embeddability.
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Research partially supported by NSF grant # DCR-8606165.
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Clote, P. (1990). The metamathematics of Fraïssé's order type conjecture. In: Ambos-Spies, K., Müller, G.H., Sacks, G.E. (eds) Recursion Theory Week. Lecture Notes in Mathematics, vol 1432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086113
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