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Varieties of Constructive Mathematics
- D. Bridges, F. Richman
- Mathematics
- 1 April 1987
1. The foundations of constructive mathematics 2. Constructive analysis 3. Russian constructive mathematics 4. Constructive algebra 5. Intuitionism 6. Contrasting varieties 7. Intuitionistic logic…
A Course in Constructive Algebra
- R. Mines, F. Richman, Wim Ruitenburg
- Mathematics
- 18 December 1987
I. Sets.- 1. Constructive vs. classical mathematics.- 2. Sets, subsets and functions.- 3. Choice.- 4. Categories.- 5. Partially ordered sets and lattices.- 6. Well-founded sets and ordinals.- Notes.-…
The fundamental theorem of algebra: a constructive development without choice
- F. Richman
- Mathematics
- 1 November 2000
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…
Intuitionism As Generalization
- F. Richman
- Philosophy
- 1 February 1990
I was inspired, not to say provoked, to write this note by Michel J. Blais's article A pragmatic analysis of mathematical realism and intuitionism [2]. Having spent the greater part of my career…
Generalized real numbers in constructive mathematics
- F. Richman
- Mathematics
- 21 December 1998
A Constructive Proof of Gleason's Theorem
- F. Richman, D. Bridges
- Mathematics
- 10 March 1999
Abstract Gleason's theorem states that any totally additive measure on the closed subspaces, or projections, of a Hilbert space of dimension greater than two is given by a positive operator of trace…
Nontrivial uses of trivial rings
- F. Richman
- Mathematics
- 1 April 1988
Four theorems about commutative rings are proved with the aid of the notion of a trivial ring. 0. Introduction. A ring R is trivial if 0 = 1 in R, that is, if R consists of a single element. Although…
Primary abelian groups as modules over their endomorphism rings
- F. Richman, E. Walker
- Mathematics
- 1 February 1965
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