Sufficient Conditions of Incompleteness for the Formalization of Parts of Arithmetic

  • N. K. Kosovskii
Part of the Seminars in Mathematics book series (SM, volume 4)


In this note some sufficient conditions on the formalization of parts of arithmetic are formulated, upon compliance with which this formalization is incomplete.


Natural Number Satisfying Condition Recursive Function Diophantine Equation Consultant Bureau 
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Literature Cited

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    Kleene, S. C., Introduction to Metamathematics. Van Nostrand, Princeton, 1950.Google Scholar
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    Robinson, J., “The undecidability of exponential diophantine equations,” in: Logic, Methodology and Philosophy of Science, Stanford, Calif., 1962, pp. 12–13.Google Scholar
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    Martsev, A. I., Algorithms and Recursive Functions, Moscow, 1965.Google Scholar
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    Robinson, R. M., “Arithmetical representation of recursively enumerable sets,” J. Symbolic Logic, 21:162–186 (1956).CrossRefGoogle Scholar
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    Davis, M., “Extensions and corollaries of recent work on Hilberths tenth problem,” Illinois J. of Math., 7:246–250 (1963).Google Scholar

Copyright information

© Consultants Bureau 1969

Authors and Affiliations

  • N. K. Kosovskii

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