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Monadic Theory of a Linear Order Versus the Theory of its Subsets with the Lifted Min/Max Operations

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Fields of Logic and Computation II

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9300))

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Abstract

We compare the monadic second-order theory of an arbitrary linear ordering L with the theory of the family of subsets of L endowed with the operation on subsets obtained by lifting the \(\max \) operation on L. We show that the two theories define the same relations. The same result holds when lifting the \(\min \) operation or both \(\max \) and \(\min \) operations.

Partially supported by TARMAC ANR agreement 12 BS02 007 01.

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Authors and Affiliations

  1. LIAFA, CNRS UMR 7089, Université Paris 7 Denis Diderot, Paris, France

    Christian Choffrut & Serge Grigorieff

Authors
  1. Christian Choffrut
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  2. Serge Grigorieff
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Corresponding author

Correspondence to Serge Grigorieff .

Editor information

Editors and Affiliations

  1. Steklov Mathematical Institute, Moscow, Russia

    Lev D. Beklemishev

  2. University of Michigan, Ann Arbor, Michigan, USA

    Andreas Blass

  3. Tel Aviv University, Tel Aviv, Israel

    Nachum Dershowitz

  4. Universität des Saarlandes, Saarbrücken, Germany

    Bernd Finkbeiner

  5. Microsoft Research, REDMOND, Washington, USA

    Wolfram Schulte

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Choffrut, C., Grigorieff, S. (2015). Monadic Theory of a Linear Order Versus the Theory of its Subsets with the Lifted Min/Max Operations. In: Beklemishev, L., Blass, A., Dershowitz, N., Finkbeiner, B., Schulte, W. (eds) Fields of Logic and Computation II. Lecture Notes in Computer Science(), vol 9300. Springer, Cham. https://doi.org/10.1007/978-3-319-23534-9_6

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  • DOI: https://doi.org/10.1007/978-3-319-23534-9_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23533-2

  • Online ISBN: 978-3-319-23534-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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