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A constructive formulation of Gleason's theorem
Journal of Philosophical Logic 26 (6):661-670 (1997)
Abstract
In this paper I wish to show that we can give a statement of a restricted form of Gleason's Theorem that is classically equivalent to the standard formulation, but that avoids the counterexample that Hellman gives in "Gleason's Theorem is not Constructively Provable"My notes
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Citations of this work
Discussion. Applied constructive mathematics: on Hellman's 'mathematical constructivism in spacetime'.H. Billinge - 2000 - British Journal for the Philosophy of Science 51 (2):299-318.
Gleason's theorem has a constructive proof.Fred Richman - 2000 - Journal of Philosophical Logic 29 (4):425-431.
Bishop's Mathematics: a Philosophical Perspective.Laura Crosilla - forthcoming - In Handbook of Bishop's Mathematics. CUP.
Fermat’s last theorem proved in Hilbert arithmetic. III. The quantum-information unification of Fermat’s last theorem and Gleason’s theorem.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (12):1-30.
A constructivist perspective on physics.Peter Fletcher - 2002 - Philosophia Mathematica 10 (1):26-42.
References found in this work
Incompleteness, Nonlocality, and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics.Michael Redhead - 1987 - New York: Oxford University Press.
Constructivism in mathematics: an introduction.A. S. Troelstra - 1988 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.. Edited by D. van Dalen.
The structure and interpretation of quantum mechanics.R. I. G. Hughes - 1989 - Cambridge, Mass.: Harvard University Press.
The Structure and Interpretation of Quantum Mechanics.R. I. G. Hughes - 1992 - Tijdschrift Voor Filosofie 54 (4):735-736.
Gleason's theorem is not constructively provable.Geoffrey Hellman - 1993 - Journal of Philosophical Logic 22 (2):193 - 203.
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