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

DOI:
https://doi.org/10.1090/S0002-9939-00-05327-2

Published electronically:
March 1, 2000

MathSciNet review:
1664313

Full-text PDF

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.**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**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
03F65,
03E25

Retrieve articles in all journals with MSC (1991): 03F65, 03E25

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:
https://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