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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A weak countable choice principle


Authors: Douglas Bridges, Fred Richman and Peter Schuster
Journal: Proc. Amer. Math. Soc. 128 (2000), 2749-2752
MSC (1991): Primary 03F65, 03E25
Published electronically: March 1, 2000
MathSciNet review: 1664313
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. Errett Bishop, Foundations of constructive analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0221878 (36 #4930)
  • 2. B. A. Kushner, Lectures on constructive mathematical analysis, Translations of Mathematical Monographs, vol. 60, American Mathematical Society, Providence, RI, 1984. Translated from the Russian by E. Mendelson; Translation edited by Lev J. Leifman. MR 773852 (86a:03067)
  • 3. Ray Mines, Fred Richman, and Wim Ruitenburg, A course in constructive algebra, Universitext, Springer-Verlag, New York, 1988. MR 919949 (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. Wim B. G. Ruitenburg, Constructing roots of polynomials over the complex numbers, Computational aspects of Lie group representations and related topics (Amsterdam, 1990) CWI Tract, vol. 84, Math. Centrum, Centrum Wisk. Inform., Amsterdam, 1991, pp. 107–128. MR 1120034 (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: http://dx.doi.org/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
Published electronically: March 1, 2000
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2000 American Mathematical Society