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Joining k- and l-recognizable sets of natural numbers

  • Roger Villemaire
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)

Abstract

We show that the first order theory of < IN, +, V k , V l >, where V r : IN{0} → IN is the function which sends x to V r (x), the greatest power of r which divides x and k, l are multiplicatively independent (i.e. they have no common power) is undecidable. Actually we prove that multiplication is definable in < IN, +, V k , V l >. This shows that the theorem of Büchi cannot be generalized to a class containing all k- and all l-recognizable sets.

Keywords

Natural Number Great Power Finite Subset Arithmetic Progression Recursive Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Roger Villemaire
    • 1
  1. 1.Département de mathématiques et d'informatiqueU.Q.A.M.MontréalCanada

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