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Well-ordering of algebras and Kruskal's theorem

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Logic, Language and Computation

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 792))

Abstract

We define well-partial-orderings on abstract algebras and give their order types. For every ordinal in an initial segment of the Bachmann hierarchy there is one and only one (up to isomorphism) algebra giving the ordinal as order type. As a corollary, we show Kruskal-type theorems for various structures are equivalent to well-orderedness of certain ordinals.

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Authors and Affiliations

  1. LIENS, 45 rue d'Ulm, 75230, Paris Cedex 05, France

    Ryu Hasegawa

  2. RIMS, Kyoto University, Sakyo-ku, 606, Kyoto, Japan

    Ryu Hasegawa

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  1. Ryu Hasegawa
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Neil D. Jones Masami Hagiya Masahiko Sato

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© 1994 Springer-Verlag Berlin Heidelberg

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Hasegawa, R. (1994). Well-ordering of algebras and Kruskal's theorem. In: Jones, N.D., Hagiya, M., Sato, M. (eds) Logic, Language and Computation. Lecture Notes in Computer Science, vol 792. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032399

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  • DOI: https://doi.org/10.1007/BFb0032399

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57935-9

  • Online ISBN: 978-3-540-48391-5

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