层逻辑、量子集合论与量子力学的解释
Sheaf Logic, Quantum Set Theory and the Interpretation of Quantum Mechanics
摘要：
基于Sheaf逻辑方法的集合论强制，量子变量集的层次结构的构造推广和简化Takeuti开发的布尔值模型的集合论的类似的建设。在这个模型上，给出了自伴算子与模型实数之间的Takeuti对应关系的两种证明。这种方法的结果是更具建设性的直接关系与Gelfand表示定理，揭示了这些结果的重要性，相对于解释量子力学密切联系的Deutsch-Everett multiplier解释。最后，它是如何在这种情况下的概念的泛型和相应的通用模型定理可以帮助解释古典的出现也与Deutsch-埃弗雷特的角度。
英文摘要：
Based on the Sheaf Logic approach to set theoretic forcing, a hierarchy of Quantum Variable Sets is constructed which generalizes and simplifies the analogous construction developed by Takeuti on boolean valued models of set theory. Over this model two alternative proofs of Takeuti's correspondence, between self adjoint operators and the real numbers of the model, are given. This approach results to be more constructive showing a direct relation with the Gelfand representation theorem, revealing also the importance of these results with respect to the interpretation of Quantum Mechanics in close connection with the Deutsch-Everett multiversal interpretation. Finally, it is shown how in this context the notion of genericity and the corresponding generic model theorem can help to explain the emergence of classicality also in connection with the Deutsch- Everett perspective.
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