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The metamathematics of Fraïssé's order type conjecture

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Recursion Theory Week

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1432))

Abstract

A well ordering has the property that any non-empty subset has a minimum element. In [Girard

  1. (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

  2. (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.

Research partially supported by NSF grant # DCR-8606165.

Statement: This article is the final version and will not be submitted for publication elsewhere.

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Authors and Affiliations

  1. Department of Computer Science, Boston College, USA

    P. Clote

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  1. P. Clote
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Klaus Ambos-Spies Gert H. Müller Gerald E. Sacks

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© 1990 Springer-Verlag

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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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  • DOI: https://doi.org/10.1007/BFb0086113

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52772-5

  • Online ISBN: 978-3-540-47142-4

  • eBook Packages: Springer Book Archive

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