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A Constructive Formulation of Gleason's Theorem

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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”.

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REFERENCES

  1. Troelstra, A. S. and van Dalen, D. (1988): Constructivism in Mathematics. North-Holland, Amsterdam.

  2. Hellman, G. (1993): Gleason's theorem is not constructively provable. Journal of Philosophical Logic 22: 193–203.

    Google Scholar 

  3. Redhead, M. (1987): Incompleteness, Nonlocality and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics.Clarendon Press, Oxford.

    Google Scholar 

  4. Keane, R., Cooke, M. and Moran, W. (1989): An elementary proof of Gleason's theorem. In [5] Appendix A.

  5. Hughes, R. I. G. (1989): The Structure and Interpretation of Quantum Mechanics. Harvard University Press, Cambridge, MA.

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  6. Lang, S. (1983): Undergraduate Analysis. Springer, New York.

    Google Scholar 

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Billinge, H. A Constructive Formulation of Gleason's Theorem. Journal of Philosophical Logic 26, 661–670 (1997). https://doi.org/10.1023/A:1004275113665

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  • DOI: https://doi.org/10.1023/A:1004275113665

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