Araki, H. (2000). Mathematical Theory of Quantum Fields. Oxford: Oxford University Press.

Bell, J. L. (2005). Set Theory: Boolean-Valued Models and Independence Proofs (third edition). Oxford: Oxford University Press.

Berberian, S. K. (1972). Baer *-Rings. Berlin: Springer.

Birkhoff, G. & von Neumann, J. (1936). The logic of quantum mechanics. Annals of Mathematics, 37, 823–843.

Bruns, G. & Kalmbach, G. (1973). Some remarks on free orthomodular lattices. In Schmidt, J., editor. Proceedings of the Lattice Theory Conference, Houston, TX, pp. 397–408.

Chevalier, G. (1989). Commutators and decompositions of orthomodular lattices. Order, 6, 181–194.

Cohen, P. J. (1963). The independence of the continuum hypothesis I. Proceedings of the National Academy of Sciences of the United States of America, 50, 1143–1148.

Cohen, P. J. (1966). Set Theory and the Continuum Hypothesis. New York: Benjamin.

Dirac, P. A. M. (1958). The Principles of Quantum Mechanics (fourth edition). Oxford: Oxford University Press.

Fourman, M. P. & Scott, D. S. (1979). Sheaves and logic. In Fourman, M. P., Mulvey, C. J., and Scott, D. S., editors. Applications of Sheaves. Lecture Notes in Mathematics, Vol. 753. Berlin: Springer, pp. 302–401.

Georgacarakos, G. N. (1979). Orthomodularity and relevance. Journal of Philosophical Logic, 8, 415–432.

Grayson, R. J. (1979). Heyting-valued models for intuitionistic set theory. In Fourman, M. P., Mulvey, C. J., and Scott, D. S., editors. Applications of Sheaves. Lecture Notes in Mathematics, Vol. 753. Berlin: Springer, pp. 402–414.

Hardegree, G. M. (1981). Material implication in orthomodular (and Boolean) lattices. Notre Dame Journal of Formal Logic, 22, 163–182.

Herman, L., Marsden, E. L., & Piziak, R. (1975). Implication connectives in orthomodular lattices. Notre Dame Journal of Formal Logic, 16, 305–328.

Husimi, K. (1937). Studies on the foundation of quantum mechanics I. Proceedings of the Physico-Mathematical Society of Japan, 19, 766–778.

Johnstone, P. T. (1977). Topos Theory. London: Academic.

Kalmbach, G. (1983). Orthomodular Lattices. London: Academic.

Kotas, J. (1967). An axiom system for the modular logic. Studia Logica, 21, 17–38.

Marsden, E. L. (1970). The commutator and solvability in a generalized orthomodular lattice. Pacific Journal of Mathematics, 33, 357–361.

Ozawa, M. (2005). Perfect correlations between noncommuting observables. Physics Letters A, 335, 11–19.

Ozawa, M. (2006). Quantum perfect correlations. Annals of Physics, 321, 744–769.

Ozawa, M. (2007). Transfer principle in quantum set theory. Journal of Symbolic Logic, 72, 625–648.

Ozawa, M. (2016). Quantum set theory extending the standard probabilistic interpretation of quantum theory. New Generation Computing, 34, 125–152.

Pulmannová, S. (1985). Commutators in orthomodular lattices. Demonstratio Mathematica, 18, 187–208.

Sasaki, U. (1954). Orthocomplemented lattices satisfying the exchange axiom. Journal of Science of the Hiroshima University: Series A, 17, 293–302.

Scott, D. & Solovay, R. (1967). Boolean-valued models for set theory.
*Unpublished manuscript for* Proceedings of AMS Summer Institute on Set Theory. Los Angeles: University of California, 1967.

Takeuti, G. (1981). Quantum set theory. In Beltrametti, E. G. and van Fraassen, B. C., editors. Current Issues in Quantum Logic. New York: Plenum, pp. 303–322.

Takeuti, G. & Zaring, W. M. (1973). Axiomatic Set Theory. New York: Springer.

Titani, S. (1999). A lattice-valued set theory. Archive for Mathematical Logic, 38, 395–421.

Titani, S. & Kozawa, H. (2003). Quantum set theory. International Journal of Theoretical Physics, 42, 2575–2602.

Urquhart, A. (1983). Review. Journal of Symbolic Logic, 48, 206–208.

von Neumann, J. (1955). Mathematical Foundations of Quantum Mechanics. Princeton, NJ: Princeton University Press. [Originally published: *Mathematische Grundlagen der Quantenmechanik* (Springer, Berlin, 1932)].