Definability in the Infix Order on Words

  • Oleg V. Kudinov
  • Victor L. Selivanov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5583)

Abstract

We develop a theory of (first-order) definability in the infix partial order on words in parallel with a similar theory for the h-quasiorder of finite k-labeled forests. 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.

Keywords

Infix order definability automorphism least fixed point first-order theory biinterpretability 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Oleg V. Kudinov
    • 1
  • Victor L. Selivanov
    • 2
  1. 1.S.L. Sobolev Institute of MathematicsSiberian Division Russian Academy of SciencesRussia
  2. 2.A.P. Ershov Institute of Informatics SystemsSiberian Division Russian Academy of SciencesRussia

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