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)


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.


Natural Number Great Power Finite Subset Arithmetic Progression Recursive Function 
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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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