Abstract
The classical theory of ordered fields (Artin-Schreier theory) makes intensive use of non-constructive methods, in particular of the axiom of choice. However since Tarski (and even since Sturm and Sylvester) one knows how to compute in the real closure of an ordered field K solely by computations in K. This apparent contradiction is solved in this paper.
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Lombardi, H., Roy, MF. (1991). Elementary constructive theory of ordered fields. In: Mora, T., Traverso, C. (eds) Effective Methods in Algebraic Geometry. Progress in Mathematics, vol 94. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0441-1_17
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DOI: https://doi.org/10.1007/978-1-4612-0441-1_17
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