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… Expand

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… Expand

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… Expand

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… Expand