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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
MathSciNet review:
1664313
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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:
- 1.
- BISHOP, ERRETT, Foundations of constructive analysis, McGraw-Hill, 1967. MR 36:4930
- 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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Additional Information:
Douglas
Bridges
Affiliation:
Department of Mathematics, University of Waikato, Hamilton, New Zealand
Address at time of publication:
Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand
Email:
douglas@math.waikato.ac.nz, d.bridges@math.canterbury.ac.nz
Fred
Richman
Affiliation:
Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431
Email:
richman@fau.edu
Peter
Schuster
Affiliation:
Mathematisches Institut, Universität München, Theresienstraße 39, München 80333, Germany
Email:
pschust@rz.mathematik.uni-muenchen.de
DOI:
10.1090/S0002-9939-00-05327-2
PII:
S 0002-9939(00)05327-2
Keywords:
Axiom of choice
Received by editor(s):
January 26, 1998
Received by editor(s) in revised form:
October 29, 1998
Posted:
March 1, 2000
Communicated by:
Carl G. Jockusch, Jr.
Copyright of article:
Copyright
2000,
American Mathematical Society
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