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A Suppes predicate for general relativity and set-theoretically generic spacetimes

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Abstract

We summarize ideas from Zermelo-Fraenkel set theory up to an axiomatic treatment for general relativity based on a Suppes predicate. We then examine the meaning of set-theoretic genericity for manifolds that underlie the Einstein equations. A physical interpretation is finally offered for those set-theoretically generic manifolds in gravitational theory.

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References

  • Augerstein, B. W. (1984).International Journal of Theoretical Physics,23, 1197.

    Google Scholar 

  • Bell, J. L. (1985).Boolean-Valued Models and Independence Proofs in Set Theory, Oxford.

  • Benioff, P. A. (1976a).Journal of Mathematical Physics,17, 618.

    Google Scholar 

  • Benioff, P. A. (1976b).Journal of Mathematical Physics,17, 629.

    Google Scholar 

  • Bott, R., and Tu, L. W. (1982).Differential Forms in Algebraic Topology, Springer.

  • Bourbaki, N. (1957).Théorie des Ensembles, Hermann, Paris.

    Google Scholar 

  • Cairns, S. S. (1940).Annals of Mathematics,41, 796.

    Google Scholar 

  • Chaitin, G. J. (1982).International Journal of Theoretical Physics,22, 941.

    Google Scholar 

  • Chaitin, G. J. (1987).Advances in Applied Mathematics,8, 119.

    Google Scholar 

  • Cheeger, J., and Kister, J. M. (1970a). Counting topological manifolds, inTopology of Manifolds, J. C. Cantrell and C. H. Edwards, Jr., eds., Markham, Chicago.

    Google Scholar 

  • Cheeger, J., and Kister, J. M. (1970b).Topology,9, 149.

    Google Scholar 

  • Cohen, P. J. (1966).Set Theory and the Continuum Hypothesis, Benjamin.

  • Cohen, P. J., and Hersh, R. (1967).Scientific American,217(12), 104.

    Google Scholar 

  • Da Costa, N. C. A., and Chuaqui, R. (1988).Erkenntnis,29, 95.

    Google Scholar 

  • Da Costa, N. C. A., and Doria, F. A. (1989a). Structures, Suppes predicates and Boolean-valued models in physics, preprint, inFestschrift in Honor of V. Smirnov, J. Hintikka, ed., to appear.

  • Da Costa, N. C. A., and Doria, F. A. (1989b). Suppes predicates for first-quantized physics, preprint.

  • Da Costa, N. C. A., and French, S. (1990). The Model-theoretic approach in the philosophy of science,Philosophy of Science, to appear.

  • De Barros, J. A. (1989). M. Sc. thesis, Brazilian Center for Physical Research [in Portuguese].

  • Doria, F. A., de Barros, J. A., and Ribeiro-da Silva, M. (1987).Bol. Soc. Paran. Matemática, 2nd Series,8, 197.

    Google Scholar 

  • Feferman, S. (1965).Fundamenta Mathematica,56, 325.

    Google Scholar 

  • Fischer, A. E. (1970). The theory of superspace, inRelativity, M. Carmeli, S. I. Fickler and L. Witten, eds., Plenum Press, New York.

    Google Scholar 

  • Freed, D. S., and Uhlenbeck, K. K. (1985).Instantons and Four-Manifolds, MSRI Publications, Springer.

    Google Scholar 

  • Hinman, P. G. (1978).Recursion-Theoretic Hierarchies, Springer.

  • Kirby, R. C. (1989).The Topology of 4-Manifolds, Springer.

  • Kneebone, G. T. (1963).Mathematical Logic and the Foundations of Mathematics, Van Nostrand.

  • Kobayashi, S., and Nomizu, K. (1963).Foundations of Differential Geometry, I, Wiley.

  • Krivine, J. L. (1969).Théorie Axiomatique des Ensembles, PUF, Paris.

    Google Scholar 

  • Kunen, K. (1983).Set Theory, North-Holland, Amsterdam.

    Google Scholar 

  • Manin, Y. (1977).A Course in Mathematical Logic, Springer.

  • Massey, W. S. (1967).Algebraic Topology: An Introduction, Harcourt-Brace & World.

  • Novikov, S., Doubrovine, B., and Fomenko, A. (1987).Géométrie Contemporaine: Méthodes et Applications, III, Mir, Moscow.

    Google Scholar 

  • Odifreddi, P. G. (1983).Journal of Symbolic Logic,48, 288.

    Google Scholar 

  • Quinn, F. (1982).Journal of Differential Geometry,17, 503.

    Google Scholar 

  • Ross, D. K. (1984).International Journal of Theoretical Physics,23, 1207.

    Google Scholar 

  • Scott, D. S. (1967).Mathematical Systems Theory,1, 89 (1967).

    Google Scholar 

  • Scott, D. S. (1985). Introduction, to J. L. Bell,Boolean-Valued Models and Independence Proofs in Set Theory, Oxford.

  • Solovay, R. M. (1970).Annals of Mathematics,92, 1.

    Google Scholar 

  • Shoenfield, J. (1971). Unramified forcing, inProceedings of the Symposium on Pure Mathematics,13, 357.

    Google Scholar 

  • Steenrod, N. (1951).The Topology of Fiber Bundles, Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • Suppes, P. (1967). Set-Theoretical Structures in Science, mimeographed notes, Stanford University.

  • Taubes, C. H. (1987).Journal of Differential Geometry,25, 363.

    Google Scholar 

  • Whitehead, J. H. C. (1940).Annals of Mathematics,41, 809.

    Google Scholar 

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Author notes

  1. F. A. Doria

    Present address: Center for the Study of Mathematical Theories of Communication, IDEA/School of Communications, Federal University of Rio de Janeiro, 22290, Rio de Janeiro RJ, Brazil

Authors and Affiliations

  1. Institute for Advanced Studies, University of São Paulo, 05508, São Paulo SP, Brazil

    N. C. A. da Costa

  2. IMSSS/Stanford University, 94305-4775, Stanford, California

    F. A. Doria

  3. Brazilian Center for Physical Research, 22290, Rio de Janeiro RJ, Brazil

    J. A. de Barros

Authors
  1. N. C. A. da Costa
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  2. F. A. Doria
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  3. J. A. de Barros
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da Costa, N.C.A., Doria, F.A. & de Barros, J.A. A Suppes predicate for general relativity and set-theoretically generic spacetimes. Int J Theor Phys 29, 935–961 (1990). https://doi.org/10.1007/BF00673682

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  • DOI: https://doi.org/10.1007/BF00673682

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