Proceedings of the American Mathematical Society

Author(s): Carlos R. Videla
Journal: Proc. Amer. Math. Soc. 127 (1999), 851-860.
MSC (1991): Primary 03C68, 11R04
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Abstract: Let $\Omega$ be the field of constructible numbers, i.e. the numbers constructed from a given unit length using ruler and compass. We prove $\widetilde{\mathbb Z}\cap\Omega$ is definable in $\Omega$ .

1.: N. Jacobson, Basic algebra I, Freeman & Co., San Francisco, 1974. MR 50:9457
2.: S. Lang, Algebraic number theory, Addison-Wesley, New York, 1970. MR 44:181
3.: A. Macintyre and A. Wilkie, On the decidability of the real exponential field, Oxford Univ., 1993, preprint.
4.: J. Neukirch, Class field theory, Springer-Verlag, New York, 1986. MR 87i:11005
5.: J. Robinson, Definability and decision problems in arithmetic, J. Symbolic Logic 14 (1949). MR 11:151f
6.: R. Rumely, Undecidability and definability for the theory of global fields, Trans. Amer. Math. Soc. 262 (1980), 195-217. MR 81m:03053
7.: A. Tarski, A decision method for elementary algebra and geometry, Rand Corporation, California, 1948. MR 10:499f
8.: C. Videla, Definability of the ring of integers of pro- $p$ extensions of number fields, in preparation.

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