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Summary:
The non-existence of hidden variables for the whole system in the formulation of Jauch and Piron can be easily deduced from the result of Zierler and Schlesinger. No further assumptions on the structure of yes - no experiments are needed.
References:
[1] J. Jauch C. Piron: Helvetica physica acta 36 (1963), 827. MR 0171511
[2] J. Jauch C. Piron: Reviews of Modern Physics 40 (1968).
[3] S. P. Gudder: ibid. Zbl 1169.81304
[4] N. Zierler M. Schlessinger: Duke Math. Journal 32 (1965), 251. MR 0175520
[5] G. Birkhoff J. von Neumann: Ann. of Math. 37 (1936), 823.
[6] J. C. T. Pool: Comm. in Math. Phys. 9 (1968), 118. DOI 10.1007/BF01645838 | MR 0229431 | Zbl 0165.28902
[7] G. Birkhoff: Lattice Theory. revised edition, N. Y. 1948. MR 0029876 | Zbl 0033.10103
[8] S. P. Gudder: Journal of Math. Phys. 11 (1970), 1037. DOI 10.1063/1.1665193 | Zbl 0326.60121
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