@book(Bel85,
 author       = {J. L. Bell},
 year         = {2005},
 title        = {Set Theory: {Boolean}-Valued Models and Independence Proofs},
 edition      = {3rd},
 publisher    = {Oxford UP},
 address      = {Oxford},
 doi          = {10.1093/acprof:oso/9780198568520.001.0001},
)
@article(BvN36,
 author       = {G. Birkhoff and J. von Neumann},
 year         = {1936},
 title        = {The Logic of Quantum Mechanics},
 journal      = {Ann.\ Math.},
 volume       = {{37}},
 pages        = {823--843},
 doi          = {10.2307/1968621},
)
@inproceedings(BK73,
 author       = {G. Bruns and G. Kalmbach},
 year         = {1973},
 title        = {Some remarks on free orthomodular lattices},
 editor       = {J. Schmidt},
 booktitle    = {Proc.\ Lattice Theory Conf.},
 address      = {Houston, U.S.A.},
 pages        = {397--408},
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@article(Che89,
 author       = {G. Chevalier},
 year         = {1989},
 title        = {Commutators and Decompositions of Orthomodular Lattices},
 journal      = {Order},
 volume       = {6},
 pages        = {181--194},
 doi          = {10.1007/BF02034335},
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@article(Coh63,
 author       = {P. J. Cohen},
 year         = {1963},
 title        = {The independence of the continuum hypothesis {I}},
 journal      = {Proc.\ Nat.\ Acad.\ Sci.\ U.S.A.},
 volume       = {{50}},
 pages        = {1143--1148},
 doi          = {10.1073/pnas.50.6.1143},
)
@book(Coh66,
 author       = {P. J. Cohen},
 year         = {1966},
 title        = {Set Theory and the Continuum Hypothesis},
 publisher    = {Benjamin},
 address      = {New York},
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@unpublished(DW12,
 author       = {A. Doering and B. Dewitt},
 year         = {2012},
 title        = {Self-adjoint Operators as Functions I: Lattices, Galois Connections, and the Spectral Order},
 url          = {https://arxiv.org/abs/1208.4724},
)
@incollection(FS79,
 author       = {M. P. Fourman and D. S. Scott},
 year         = {1979},
 title        = {Sheaves and logic},
 editor       = {M. P. Fourman and C. J. Mulvey and D. S. Scott},
 booktitle    = {Applications of Sheaves: Proceedings of the Research Symposium on Applications of Sheaf Theory to Logic, Algebra, and Analysis, Durham, July 9-21, 1977},
 series       = {Lecture Notes in Math.\ {\bf753}},
 publisher    = {Springer},
 address      = {Berlin},
 pages        = {302--401},
 doi          = {10.1007/BFb0061824},
)
@incollection(Gra79,
 author       = {R. J. Grayson},
 year         = {1979},
 title        = {Heyting-valued models for intuitionistic set theory},
 editor       = {M. P. Fourman and C. J. Mulvey and D. S. Scott},
 booktitle    = {Applications of Sheaves: Proceedings of the Research Symposium on Applications of Sheaf Theory to Logic, Algebra, and Analysis, Durham, July 9-21, 1977},
 series       = {Lecture Notes in Math.\ {753}},
 publisher    = {Springer},
 address      = {Berlin},
 pages        = {402--414},
 doi          = {10.1007/BFb0061825},
)
@article(Gud68,
 author       = {S. Gudder},
 year         = {1969},
 title        = {Joint Distributions of Observables},
 journal      = {Indiana Univ. Math. J.},
 volume       = {18},
 pages        = {325--335},
 doi          = {10.1512/iumj.1969.18.18025},
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@article(Har81,
 author       = {G. M. Hardegree},
 year         = {1981},
 title        = {Material implication in orthomodular {(and Boolean)} lattices},
 journal      = {Notre Dame J. Formal Logic},
 volume       = {22},
 pages        = {163--182},
 doi          = {10.1305/ndjfl/1093883401},
)
@book(Joh77,
 author       = {P. T. Johnstone},
 year         = {1977},
 title        = {Topos theory},
 series       = {London Mathematical Society Monographs, vol. 10},
 publisher    = {Academic},
 address      = {London},
)
@book(Kal83,
 author       = {G. Kalmbach},
 year         = {1983},
 title        = {Orthomodular Lattices},
 publisher    = {Academic},
 address      = {London},
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@article(Mar70,
 author       = {E. L. Marsden},
 year         = {1970},
 title        = {The commutator and solvability in a generalized orthomodular lattice},
 journal      = {Pacific J.\ Math},
 volume       = {33},
 pages        = {357--361},
 doi          = {10.2140/pjm.1970.33.357},
)
@book(vN55,
 author       = {J. von {Neumann}},
 year         = {1955},
 title        = {Mathematical Foundations of Quantum Mechanics},
 publisher    = {Princeton UP},
 address      = {Princeton, NJ},
 note         = {[Originally published: {\it Mathematische Grundlagen der Quantenmechanik} (Springer, Berlin, 1932)]},
)
@article(Ols71,
 author       = {M. P. Olson},
 year         = {1971},
 title        = {The selfadjoint operators of a von Neumann algebra form a conditionally complete lattice},
 journal      = {Proc.~Amer.~Math.~Soc.},
 volume       = {28},
 number       = {2},
 pages        = {537--544},
 doi          = {10.1090/S0002-9939-1971-0276788-1},
)
@article(06QPC,
 author       = {M. Ozawa},
 year         = {2006},
 title        = {Quantum perfect correlations},
 journal      = {Ann.\ Physics},
 volume       = {321},
 pages        = {744--769},
 doi          = {10.1016/j.aop.2005.08.007},
)
@article(07TPQ,
 author       = {M. Ozawa},
 year         = {2007},
 title        = {Transfer principle in quantum set theory},
 journal      = {J. Symbolic Logic},
 volume       = {72},
 pages        = {625--648},
 doi          = {10.2178/jsl/1185803627},
)
@article(16A2,
 author       = {M. Ozawa},
 year         = {2016},
 title        = {Quantum Set Theory Extending the Standard Probabilistic Interpretation of Quantum Theory},
 journal      = {New Generat.\ Comput.},
 volume       = {{\bf34}},
 pages        = {125--152},
 doi          = {10.1007/s00354-016-0205-2},
)
@article(PS12,
 author       = {P{\l}aneta, A. and J. Stochel},
 year         = {2012},
 title        = {Spectral order for unbounded operators},
 journal      = {J. Math.~Anal.~App.},
 volume       = {389},
 number       = {2},
 pages        = {1029--1045},
 doi          = {10.1016/j.jmaa.2011.12.042},
)
@article(Pul85,
 author       = {S. Pulmannov\'{a}},
 year         = {1985},
 title        = {Commutators in orthomodular lattices},
 journal      = {Demonstratio Math.},
 volume       = {18},
 pages        = {187--208},
)
@unpublished(SS67,
 author       = {D. Scott and R. Solovay},
 title        = {Boolean-Valued Models for Set Theory},
 note         = {Unpublished manuscript for {\em Proc. AMS Summer Institute on Set Theory}, Los Angeles: Univ.\ Cal., 1967},
)
@incollection(Ta81,
 author       = {G. Takeuti},
 year         = {1981},
 title        = {Quantum set theory},
 editor       = {E. G. Beltrametti and B. C. van Fraassen},
 booktitle    = {Current Issues in Quantum Logic},
 publisher    = {Plenum},
 address      = {New York},
 pages        = {303--322},
 doi          = {10.1007/978-1-4613-3228-2_19},
)