A Topos for Algebraic Quantum Theory

@article{Heunen2009ATF,
  title={A Topos for Algebraic Quantum Theory},
  author={Chris Heunen and Nicolaas P. Landsman and Bas Spitters},
  journal={Communications in Mathematical Physics},
  year={2009},
  volume={291},
  pages={63-110}
}
The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr’s idea that the empirical content of quantum physics is accessible only through classical physics, we show how a noncommutative C*-algebra of observables A induces a topos $${\mathcal{T}(A)}$$ in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra $${\underline{A… 

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