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Beyond Gödel's Theorem: Turing Nonrigidity Revisited

Published online by Cambridge University Press:  24 March 2017

S. B. Cooper
Affiliation:
School of Mathematics University of Leeds
Johann A. Makowsky
Affiliation:
Technion - Israel Institute of Technology, Haifa
Elena V. Ravve
Affiliation:
Technion - Israel Institute of Technology, Haifa
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Publisher: Cambridge University Press
Print publication year: 2017

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References

Bell., J.S. On the Einstein-Podolsky-Rosen paradox. Physics 1 (1964), 195–200; reprinted in Bell, J.S. Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, 1987, pp. 14–21.
Bohm, D. and Hiley, B.J. The Undivided Universe: An ontological interpretation of quantum theory. Routledge, London, New York, 1993.
Cooper., S.B. Definability and global degree theory. In Oikkonen, J. and Väänänen, J. eds., Logic Colloquium –90, Lecture Notes in Logic vol. 2, Springer-Verlag, Berlin, Heidelberg, New York, pp. 25-45.
Cooper., S.B. Beyond Gödel's Theorem: The failure to capture information content. In Sorbi, A. editor, Complexity, Logic and Recursion Theory, Lecture Notes in Pure and Applied Mathematics, vol. 187, Marcel Dekker, 1997, pp. 93–122.Google Scholar
Cooper., S.B. On a conjecture of Kleene and Post. To appear.
Cooper., S.B. The Turing universe is not rigid. To appear.
Cooper., S.B. Observation, understanding and Turing definability. In preparation.
Cooper., S.B. Turing nonrigidity and quantum theory. In preparation.
Davies, P.C.W. Why is the physical world so comprehensible? In Zurek, W.H. ed., Complexity, Entropy, and the Physics of Information, Santa Fe Inst. Studies in the Sciences of Complexity, vol. 8, Addison-Wesley, Reading, Mass., 1990, pp. 61–70.
Einstein, A. Podolsky, B. and Rosen, N. Phys. Rev., 47 (1935), 777–780.Google Scholar
Everett, H. III. “Relative state” formulation of quantum mechanics. Rev. Mod. Phys., 29 (1957), 454–462.Google Scholar
Feynman, R.P. Leighton, R.B. Sands, M. The Feynman Lectures on Physics, Vol. III. Addison-Wesley, Reading, Mass., 1965.
Feynman, R.P. and Hibbs, A.R. Quantum Mechanics and Path Integrals. McGraw-Hill, New York, London, Sydney, 1965.
Gell-Mann, M. and Hartle, J.B. Quantum mechanics in the light of quantum cosmology. In Zurek, W.H. ed., Complexity, Entropy, and the Physics of Information, Santa Fe Inst. Studies in the Sciences of Complexity, vol. 8, Addison-Wesley, Reading, Mass., 1990, pp. 425–458.
Gödel, K. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatsh. Math. Phys., 38 (1931), 173–198.Google Scholar
Gödel, K. On undecidable propositions of formal mathematical systems. Mimeographed notes, 1934; reprinted in Davis, M. editor, The Undecidable. Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions, Raven Press, New York, 1965, pp. 39–71.
Gross, P.R. and Levitt, N. Higher Superstition: The academic left and its quarrels with science. John Hopkins University Press, 1994.
Hartle, J.B. and Hawking, S.W. Wave function of the universe. Phys. Rev., D28(1983), 2960-2975.Google Scholar
Hawking, S.W. and Penrose, R. The singularities of gravitational collapse and cosmology. Proc. Roy. Soc. London, A314 (1970), 529–48.
Hawking, S.W. and Penrose, R. The Nature of Space and Time. Princeton University Press, Princeton, N.J., 1996.
Heisenberg, W. Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys., 43 (1927), 172–198.Google Scholar
Hénon, M. and Pomeau, Y. Two strange attractors with a simple structure. In Temam, R. ed., Turbulence and Navier Stokes Equations, Lecture Notes in Mathematics, vol. 565, Springer-Verlag, Berlin, Heidelberg, New York, 1976, pp. 29–68.
Jockusch, C.G. Jr. and Shore, R.A. Pseudo jump operators II: Transfinite iterations, hierarchies, and minimal covers. J. Symbolic Logic, 49 (1984), 1205–1236.Google Scholar
Kučera, A. Randomness and generalizations of fixed point free functions. In Ambos-Spies, K. Müller, G. and Sacks, G.E. eds., Recursion Theory Week, Proceedings Oberwolfach 1989, Springer, Berlin, 1990, pp. 245–254.
Lerman, M. Embedding partial lattices into the computably enumerable degrees. To appear.
Nerode, A. and Shore, R.A. Reducibility orderings: theories, definability and automorphisms. Ann. MathLogic, 18 (1980), 61–89.Google Scholar
Nies, A. Shore, R.A. and Slaman, T.A. Definability in the recursively enumerable degrees. To appear.
Odifreddi, P. Classical Recursion Theory. North-Holland, Amsterdam, New York, Oxford, 1989.
Omnès, R. The Interpretation of Quantum Mechanics. Princeton University Press, Princeton, N.J., 1994.
Penrose., R. Quantum physics and conscious thought. In Hiley, B. J. and Peat, F.D. editors, Quantum Implications: Essays in honour of David Bohm, Routledge & Kegan Paul, London, New York, 1987, pp. 105–120.
Pour-El, M.B. and Richards, I. The wave equation with computable initial data such that its unique solution is not computable. Advances in Math., 39 (1981), 215–239.Google Scholar
Pour-El, M.B. and Richards, J.I. Computability in Analysis and Physics. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1989.
Quine, W.V.O. Two dogmas of empiricism. In Quine, W.V.O. From A Logical Point Of View, Harvard University Press, Cambridge, Mass, and London, 1953, pp. 20–46.
Sacks., G.E. On the degrees less than 0′. Ann. of Math. (2) 77 (1963), 211–231.Google Scholar
Shannon, C.E. and Weaver, W. The mathematical theory of communication. University of Illinois Press, 1949.
Slaman, T.A. and Woodin, W.H. Definability in Degree Structures. To appear.
Soare, R.I. Recursively Enumerable Sets and Degrees. Springer-Verlag, Berlin, Heidelberg, London, New York, 1987.
Solomonoff., R.J. A formal theory of inductive inference. Part I. Infor. and Control 7 (1964), 1-22.Google Scholar
Turing., A.M. Systems of logic based on ordinals. Proc. London Math. Soc, 45 (1939), 161–228; reprinted in Davis, M. editor, ‘The Undecidable. Basic Papers on Vndecidable Propositions, Unsolvable Problems, and Computable Functions’, Raven Press, New York, 1965, pp. 154–222.

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