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A weak countable choice principle

Author(s): Douglas Bridges; Fred Richman; Peter Schuster
Journal: Proc. Amer. Math. Soc. 128 (2000), 2749-2752.
MSC (1991): Primary 03F65, 03E25
Posted: March 1, 2000
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Abstract: A weak choice principle is introduced that is implied by both countable choice and the law of excluded middle. This principle suffices to prove that metric independence is the same as linear independence in an arbitrary normed space over a locally compact field, and to prove the fundamental theorem of algebra.

References:

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2.: KUSHNER, BORIS A., Lectures on constructive mathematical analysis, AMS Translations 60, 1984. MR 86a:03067
3.: MINES, RAY, FRED RICHMAN AND WIM RUITENBURG, A course in constructive algebra, Springer-Verlag, 1988. MR 89d:03066
4.: RICHMAN, FRED, The fundamental theorem of algebra: a constructive development without choice, Pacific J. Math. (to appear), http:// www.math.fau.edu/ Richman/ html/docs.htm
5.: RUITENBURG, WIM B. G., Constructing roots of polynomials over the complex numbers. Computational aspects of Lie group representations and related topics (Amsterdam, 1990), 107-128, CWI Tract, 84, Math. Centrum, Centrum Wisk. Inform., Amsterdam, 1991. MR 92g:03085


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