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Definability in the Subword Order

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Programs, Proofs, Processes (CiE 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6158))

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Abstract

We develop a theory of (first-order) definability in the subword partial order in parallel with similar theories for the h-quasiorder of finite k-labeled forests and for the infix order. In particular, any element is definable (provided that words of length 1 or 2 are taken as parameters), the first-order theory of the structure is atomic and computably isomorphic to the first-order arithmetic. We also characterize the automorphism group of the structure and show that any arithmetical predicate invariant under the automorphisms of the structure is definable in the structure.

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Author information

Authors and Affiliations

  1. S.L. Sobolev Institute of Mathematics, Siberian Division, Russian Academy of Sciences,  

    Oleg V. Kudinov

  2. A.P. Ershov Institute of Informatics Systems, Siberian Division, Russian Academy of Sciences,  

    Victor L. Selivanov & Lyudmila V. Yartseva

Authors
  1. Oleg V. Kudinov
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  2. Victor L. Selivanov
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  3. Lyudmila V. Yartseva
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Editor information

Editors and Affiliations

  1. Departamento de Matemática, Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016, Lisboa, Portugal

    Fernando Ferreira

  2. Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, P.O. Box 94242, 1090, Amsterdam, GE, The Netherlands

    Benedikt Löwe

  3. Departamento de Informática e Ingeniería de Sistemas, Universidad de Zaragoza, María de Luna 1, 50018, Zaragoza, Spain

    Elvira Mayordomo

  4. Universidade dos Açores, Campus de Ponta Delgada, Apartado 1422, 9501-801, Ponta Delgada, Açores, Portugal

    Luís Mendes Gomes

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Kudinov, O.V., Selivanov, V.L., Yartseva, L.V. (2010). Definability in the Subword Order. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_28

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  • DOI: https://doi.org/10.1007/978-3-642-13962-8_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13961-1

  • Online ISBN: 978-3-642-13962-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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