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Definability in number fields

Published online by Cambridge University Press:  12 March 2014

S. P. Tung
S. P. Tung*
Affiliation:
Department of Mathematics, Chung Yuan Christian University, Chung Li, Taiwan 32023, Republic of China
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Abstract

We study the sets definable in an algebraic number field by first order formulas of various simple types, showing in particular that N and Z do not have very simple definitions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 52 , Issue 1 , March 1987 , pp. 152 - 155
Copyright
Copyright © Association for Symbolic Logic 1987

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Footnotes

1

I am very grateful to the referee for his help in making this paper readable.

References

REFERENCES

[1] Davis, M., Matijasevič, Y., and Robinson, J., Hilbert's tenth problem. Diophantine equations: positive aspects of a negative solution, Mathematical developments arising from Hilbert problems, Proceedings of Symposia in Pure Mathematics, vol. 28, American Mathematical Society, Providence, Rhode Island, 1976, pp. 323–378.CrossRefGoogle Scholar
[2] Robinson, J., Definability and decision problems in arithmetic, this Journal, vol. 14 (1949), pp. 98–114.Google Scholar
[3] Robinson, J., The undecidability of algebraic rings and fields, Proceedings of the American Mathematical Society, vol. 10 (1959), pp. 950–957.CrossRefGoogle Scholar
[4] Robinson, R. M., Arithmetical definitions in the ring of integers, Proceedings of the American Mathematical Society, vol. 2 (1951), pp. 279–284.CrossRefGoogle Scholar
[5] Robinson, R. M., Arithmetical definability of field elements, this Journal, vol. 16 (1951), pp. 125–126.Google Scholar
[6] Schinzel, A., Selected topics on polynomials, University of Michigan Press, Ann Arbor, Michigan, 1982.CrossRefGoogle Scholar
[7] Tung, S. P., On weak number theories, Japanese Journal of Mathematics, vol. 11 (1985), pp. 203–232.Google Scholar