References

  1. David Z. Albert (2010): Probability in the Everett picture. In: Simon Saunders, Jonathan Barrett, Adrian Kent & David Wallace: Many Worlds? Everett, quantum theory, and reality. Oxford University Press, Oxford, doi:10.1093/acprof:oso/9780199560561.003.0013.
  2. Max Born (1926): Zur quantenmechanik der stoßvorgänge. Zeitschrift für Physik 37(12), pp. 863–867, doi:10.1007/BF01397477.
  3. Mark S. Burgin (1983): Inductive Turing machines. Notices of the Academy of Sciences of the USSR 270(6), pp. 1289–1293.
  4. Paul Busch (2003): Quantum states and generalized observables: a simple proof of Gleason's theorem. Physics Review Letters 91(120403), doi:10.1103/PhysRevLett.91.120403.
  5. David Deutsch (1999): Quantum Theory of Probability and Decisions. Proceedings of the Royal Society of London A 455(1988), pp. 3129–3137, doi:10.1098/rspa.1999.0443.
  6. Hugh Everett III (1957): `Relative state' formulation of quantum mechanics. Reviews of Modern Physics 29, pp. 454–462, doi:10.1103/RevModPhys.29.454.
  7. E. Farhi, J. Goldstone & S. Gutmann (1989): How probability arises in quantum mechanics. Annals of Physics 192, pp. 368–382, doi:10.1016/0003-4916(89)90141-3.
  8. Andrew M. Gleason (1957): Measures on the closed subspaces of a Hilbert space. Journal of Mathematics and Mechanics 6(6), pp. 885–893, doi:10.1512/iumj.1957.6.56050.
  9. Kurt Gödel (1967): On formally undecidable propositions of Principia Mathematica and related systems I. In: J van Heijenoort: From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931. Harvard University Press, pp. 592–617, doi:10.1016/j.hm.2003.07.003.
  10. E. Mark Gold (1965): Limiting recursion. Journal of Symbolic Logic 30(1), pp. 28–48, doi:10.2307/2270580.
  11. Neill Graham (1973): The measure of relative frequency. In: The Many Worlds Interpretation of Quantum Mechanics. Princeton University Press, Princeton, pp. 229–253, doi:10.1515/9781400868056.
  12. Sam Gutmann (1995): Using classical probability to guarantee properties of infinite quantum sequences. Physical Review A 52(5), pp. 3560–3562, doi:10.1103/PhysRevA.52.3560.
  13. James B. Hartle (1968): Quantum Mechanics of Individual Systems. American Journal of Physics 36(8), pp. 704–712, doi:10.1119/1.1975096.
  14. Adrian Kent (1990): Against many worlds interpretations. International Journal of Modern Physics A 5(9), pp. 1745–1762, doi:10.1142/S0217751X90000805.
  15. Fabrizio Logiurato & Augusto Smerzi (2012): Born Rule and Noncontextual Probability 1202.2728, doi:10.4236/jmp.2012.311225.
  16. Arnold Neumaier (1999): On the many-worlds interpretation. Available at http://www.mat.univie.ac.at/~neum/manyworlds.txt.
  17. Hilary Putnam (1965): Trial and error predicates and the solution to a problem of Mostowski. Journal of Symbolic Logic 30(1), pp. 49–57, doi:10.2307/2270581.
  18. Allan F. Randall (2006): Limit recursion and Gödel's incompleteness theorem. MA thesis. York University. Available at http://allanrandall.ca/Godel.pdf.
  19. Allan F. Randall (2014): An Algorithmic Interpretation of Quantum Probability. York University, Toronto, doi:10315/27640.
  20. Erwin Schrödinger (1935): Die gegenwärtige situation in der Quantenmechanik. Naturwissenschaften 23, pp. 807–812,823–828,844–849, doi:10.1007/BF01491914.
  21. Ray Solomonoff (1960): A Preliminary Report on a General Theory of Inductive Inference. Zator Company and United States Air Force Office of Scientific Research, ZTB-138, Cambridge.
  22. Ray Solomonoff (1964): A formal theory of inductive inference. Part I. Information and Control 7, pp. 1–22, doi:10.1016/S0019-9958(64)90223-2.
  23. Ray Solomonoff (1964): A formal theory of inductive inference. Part II. Information and Control 7, pp. 224–254, doi:10.1016/S0019-9958(64)90131-7.
  24. Ray Solomonoff (1978): Complexity-based induction systems: comparisons and convergence theorems. IEEE Transactions on Information Theory 24(4), pp. 422–432, doi:10.1109/TIT.1978.1055913.
  25. Euan J. Squires (1990): On an alleged `proof' of the quantum probability law. Physics Letters A 145(2,3), pp. 67–68, doi:10.1016/0375-9601(90)90192-Q.
  26. David Wallace (2010): How to prove the Born rule. In: S. Saunders, J. Barrett, A. Kent & D. Wallace: Many Worlds? Everett, Quantum Theory, and Reality. Oxford University Press, Oxford, pp. 227–263, doi:10.1093/acprof:oso/9780199560561.003.0010.
  27. Wojciech Hubert Zurek (2005): Probabilities from Entanglement, Born's Rule from Envariance. Physics Review A 71, pp. 052105, doi:10.1103/PhysRevA.71.052105.

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