The irrationals are not recursively enumerable
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- by Richard Mansfield PDF
- Proc. Amer. Math. Soc. 110 (1990), 495-497 Request permission
Abstract:
The set of rationals is not recursive over any field of infinite transcendence degree.References
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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.
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- Harvey Friedman and Richard Mansfield, Algorithmic procedures, Trans. Amer. Math. Soc. 332 (1992), no. 1, 297–312. MR 1055807, DOI 10.1090/S0002-9947-1992-1055807-7
- Handbook of mathematical logic, Studies in Logic and the Foundations of Mathematics, vol. 90, North-Holland Publishing Co., Amsterdam, 1977. With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra. MR 457132
Additional Information
- © Copyright 1990 American Mathematical Society
- 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