The fundamental theorem of algebra: a constructive development without choice

Fred Richman

Vol. 196 (2000), No. 1, 213–230

DOI: 10.2140/pjm.2000.196.213

Abstract

Is it reasonable to do constructive mathematics without the axiom of countable choice? Serious schools of constructive mathematics all assume it one way or another, but the arguments for it are not compelling. The fundamental theorem of algebra will serve as an example of where countable choice comes into play and how to proceed in its absence. Along the way, a notion of a complete metric space, suitable for a choiceless environment, is developed.

Milestones

Received: 14 January 1998

Revised: 28 October 1998

Published: 1 November 2000