Gödel’s incompleteness theorem

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


In this section we show how the syntax of formal languages reduces in principle to arithmetic. We do this by identifying the symbols, expressions, and texts in a finite or countable alphabet A with certain natural numbers (i.e., by numbering them) in such a way that the syntactic operations (juxtaposition, substitution, etc.) are represented by recursive functions, and the syntactic relations (occurrence in an expression, “being a formula,” etc.) are represented by decidable or enumerable sets.


Partial Function Recursive Function Atomic Formula Diophantine Equation Incompleteness Theorem 
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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