Diophantine sets and algorithmic undecidability

  • Yu. I. Manin
Part of the Graduate Texts in Mathematics book series (GTM, volume 53)


In §4 of Chapter V we showed that enumerable sets are the same thing as projections of level sets of primitive recursive functions. The projections of the level sets of a special kind of primitive recursive function—polynomials with coefficients in Z +—are called Diophantine sets. We note that this class does not become any larger if we allow the coefficients in the polynomial to lie in Z. The basic purpose of this chapter is to prove the following deep result:


Prime Number Recursive Function Diophantine Equation Kolmogorov Complexity Versal Family 
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 Science+Business Media New York 1977

Authors and Affiliations

  • Yu. I. Manin
    • 1
  1. 1.V. A. Steklov Mathematical Institute of the Academy of SciencesMoscowUSSR

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