2011/11/11 by Jose Benavides, J. Benavides, Benavides, J.
Computer Science · Mathematics · Physics and Astronomy · Psychology · #03C90 (Secondary) #03E40 (Primary) 81Q10 #81P10 #Computability, Logic, AI Algorithms #FOS: Mathematics #FOS: Physical sciences #Logic (math.LO) #Mathematical Physics (math-ph) #Philosophy and Theoretical Science #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.LO #math.MP #msc:03C90 #msc:03E40 #msc:81P10 #msc:81Q10 #quant-ph
paper · pdf · doi:10.48550/arxiv.1111.2704
34 pages, 2 figures
openalex publication_date 2011/11/11 · arxiv created 2012/02/07 · arxiv updated 2012/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.