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The irrationals are not recursively enumerable


Author: Richard Mansfield
Journal: Proc. Amer. Math. Soc. 110 (1990), 495-497
MSC: Primary 03D75; Secondary 68Q15
DOI: https://doi.org/10.1090/S0002-9939-1990-1019752-9
MathSciNet review: 1019752
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Abstract: The set of rationals is not recursive over any field of infinite transcendence degree.


References [Enhancements On Off] (What's this?)

  • [BSS] L. Blum, M. Shub, and S. Smale, On a theory of computation over the real numbers; NP completeness, recursive functions and universal machines, preprint, 1987.
  • [F] H. Friedman, Algorithmic procedures, generalized Turing algorithms and elementary recursion theories, in Logic Colloquium 1969 (R. O. Gandy and C. E. M. Yates, eds.), North-Holland, Amsterdam, 1971, pp. 361-390. MR 0304140 (46:3275)
  • [FM] H. Friedman and R. Mansfield, Algorithmic procedures, preprint, 1988. MR 1055807 (92j:03042)
  • [KM] A. Kechris and Y. Moschovakis, Recursion in higher types, in Handbook of Mathematical Logic (Jon Barwise, ed.), North-Holland, 1977, pp. 681-738. MR 0457132 (56:15351)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1019752-9
Article copyright: © Copyright 1990 American Mathematical Society

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