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Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories.
G. Birkhoff, J. von Neumann, “The logic of quantum mechanics”, Ann. of Math. 37
1936
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M. H. Stone, “The theory of representations for Boolean algebras”, Trans. Amer. Math. Soc. 40
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S. Kochen, E. P. Specker, “The problem of hidden variables in quantum mechanics”, Journal of Mathematics and Mechanics 17
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M. P. Olson, “The Selfadjoint Operators of a von Neumann Algebra Form a Conditionally Complete Lattice”, Proc. of the AMS 28
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R. Goldblatt, Topoi, The Categorical Analysis of Logic
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J. Lambek, P. J. Scott, Introduction to higher order categorical logic
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J. L. Bell, Toposes and Local Set Theories
1988
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S. Mac Lane, I. Moerdijk, Sheaves in Geometry and Logic, A First Introduction to Topos Theory
1992
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C. J. Isham “Topos Theory and Consistent Histories: The Internal Logic of the Set of all Consistent Sets”, Int. J. Theor. Phys. 36
1997
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S. Mac Lane, Categories for the Working Mathematician
1997
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C. J. Isham, J. Butterfield, “A topos perspective on the Kochen-Specker theorem: I. Quantum states as generalised valuations”, Int. J. Theor. Phys. 37
1998
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C. J. Isham, J. Butterfield, “A topos perspective on the Kochen-Specker theorem: II. Conceptual aspects, and classical analogues”, Int. J. Theor. Phys. 38
1999
Cited alongside, same era.
C. J. Isham, J. Butterfield, “Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity”, Found. Phys. 30
2000
Cited alongside, same era.
C. J. Isham, J. Butterfield, “A topos perspective on the Kochen-Specker theorem: IV. Interval valuations”, Int. J. Theor. Phys. 41
2002
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P. T. Johnstone, Sketches of an Elephant, A Topos Theory Compendium
2002
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P. T. Johnstone, Sketches of an Elephant, A Topos Theory Compendium
2002
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F. W. Lawvere, R. Rosebrugh, Sets for Mathematicians
2003
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A. Döring, “Kochen-Specker Theorem for von Neumann Algebras”, Int. J. Theor. Phys. 44
2005
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H. F. de Groote, “On a canonical lattice structure on the effect algebra of a von Neumann algebra”, quant-ph/0410018 v2 (2005)
2005
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C. J. Isham, J. Butterfield, J. Hamilton, “A topos perspective on the Kochen-Specker theorem: III. Von Neumann algebras as the base category”, Int. J. Theor. Phys. 39
2000
Cited alongside, same era.
R. V. Kadison, J. R. Ringrose, Fundamentals of the Theory of Operator Algebras
2000
Cited alongside, same era.
A. Döring, C. J. Isham, “A Topos Foundation for Theories of Physics: I. Formal Languages for Physics”, quant-ph/0703060
Cited in the paper.
A. Döring, C. J. Isham, “A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory”, quant-ph/0703062
Cited in the paper.
A. Döring, C. J. Isham, “A Topos Foundation for Theories of Physics: III. The Representation of Physical Quantities with Arrows δ o ( A ) : Σ ¯ → ℝ ⪰ ¯ \delta^{o}(A):\underline{\Sigma}\rightarrow\underline{\mathbb{R}^{\succeq}} ”, quant-ph/0703064
Cited in the paper.
A. Döring, C. J. Isham, “A Topos Foundation for Theories of Physics: IV. Categories of Systems”, quant-ph/0703066
Cited in the paper.
H. F. de Groote, “Observables”, math-ph/0507019
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B. Banaschewski, C. J. Mulvey, “A globalisation of the Gelfand duality theorem”, Ann. of Pure and Applied Logic 137
2006
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