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.

**1.**Errett Bishop,*Foundations of constructive analysis*, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR**0221878****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****3.**Ray Mines, Fred Richman, and Wim Ruitenburg,*A course in constructive algebra*, Universitext, Springer-Verlag, New York, 1988. MR**919949****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**

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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

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