Quantum Set Theory |
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Authors: | Satoko Titani Haruhiko Kozawa |
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Institution: | (1) Research Institute for Information Science, Department of Natural Science and Mathematics, Chubu University, Kasugai, Aich, Japan;(2) Department of Applied Physics, Chubu University, Kasugai, Aich, Japan |
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Abstract: | The complete orthomodular lattice of closed subspaces of a Hilbert space is considered as the logic describing a quantum physical system, and called a quantum logic. G. Takeuti developed a quantum set theory based on the quantum logic. He showed that the real numbers defined in the quantum set theory represent observables in quantum physics. We formulate the quantum set theory by introducing a strong implication corresponding to the lattice order, and represent the basic concepts of quantum physics such as propositions, symmetries, and states in the quantum set theory. |
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Keywords: | quantum logic set theory lattice-valued universe |
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