Abstract
Gleason's theorem for R 3 says that if f is a nonnegative function on the unit sphere with the property that f(x) + f(y) + f(z) is a fixed constant for each triple x,y,z of mutually orthogonal unit vectors, then f is a quadratic form. We examine the issues raised by discussions in this journal regarding the possibility of a constructive proof of Gleason"s theorem in light of the recent publication of such a proof.
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Richman, F. Gleason's Theorem Has a Constructive Proof. Journal of Philosophical Logic 29, 425–431 (2000). https://doi.org/10.1023/A:1004791723301
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DOI: https://doi.org/10.1023/A:1004791723301