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A logic road from special relativity to general relativity

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Abstract

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we “derive” an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

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References

  • Andréka H., Goranko V., Mikulás Sz., Németi I., Sain I. (1995) Effective first order temporal logics. In: Bolc L., Szałas A. (eds) Time and logic, a computational approach. UCL, London, pp 51–129

    Google Scholar 

  • Andréka, H., Madarász, J. X., & Németi, I. (2002). On the logical structure of relativity theories. E-book, Alfréd Rényi Institute of Mathematics, Budapest. With contributions from A. Andai, G. Sági, I. Sain, Cs. Tőke. http://www.math-inst.hu/pub/algebraic-logic/olsort.html. (pp. 1312)

  • Andréka H., Madarász J. X., Németi I. (2006) Logical axiomatizations of space-time. Samples from the literature. In: Prékopa A., Molnár E. (eds) Non-Euclidean geometries. Springer-Verlag, New York, pp 155–185

    Chapter  Google Scholar 

  • Andréka H., Madarász J. X., Németi I. (2007) Logic of space-time and relativity theory. In: Aiello M., Pratt-Hartmann I., van Benthem J. (eds) Handbook of spatial logics. Springer-Verlag, Dordrecht, pp 607–711

    Chapter  Google Scholar 

  • Andréka, H., Madarász, J. X., Németi, I., & Székely, G. (2010). Relativity theory on logical grounds. Budapest: Course Notes. http://www.math-inst.hu/pub/algebraic-logic/kurzus10/kurzus10.htm.

  • Andréka, H., Madarász, J. X., Németi, I., Németi, P., & Székely, G. Vienna Circle and logical analysis of relativity theory. In: F. Stadler (Ed.), Wiener Kreis und Ungarn. Veröffentlishungen des Instituts Wiener Kreis, Springer–Verlag, to appear.

  • Benda T. (2008) A formal construction of the spacetime manifold. Journal of Philosophical Logic 37(5): 441–478

    Article  Google Scholar 

  • Chang C. C., Keisler H. J. (1990) Model theory. North-Holland Publishing Co, Amsterdam

    Google Scholar 

  • d’Inverno R. (1992) Introducing Einstein’s relativity. Oxford University Press, New York

    Google Scholar 

  • Einstein, A. (2006). Relativity. The special and the general theory Penguin Classics. Translated by W. Lawson (original publication in German 1921).

  • Enderton H. B. (1972) A mathematical introduction to logic. Academic Press, New York

    Google Scholar 

  • Goldblatt R. (1984) Orthogonality and spacetime geometry. Springer-Verlag, New York

    Google Scholar 

  • Henkin L., Monk J. D., Tarski A. (1971) Cylindric algebras. Part I. North-Holland Publishing Co, Amsterdam

    Google Scholar 

  • Hodges W. (1993) Model theory, Encyclopedia of mathematics and its applications. Cambridge University Press, Cambridge

    Google Scholar 

  • Madarász, J. X. (2002). Logic and relativity (in the light of definability theory). PhD thesis, Budapest: Eötvös Loránd Univ. http://www.math-inst.hu/pub/algebraic-logic/Contents.html.

  • Madarász J. X., Németi I., Székely G. (2006) Twin paradox and the logical foundation of relativity theory. Foundations of Physics 36(5): 681–714

    Article  Google Scholar 

  • Misner C. W., Thorne K. S., Wheeler J. A. (1973) Gravitation. W. H. Freeman and Co, San Francisco

    Google Scholar 

  • Rosinger, E. E. (2008). Two essays on the Archimedean versus non-Archimedean debate. arXiv:0809.4509v3.

  • Rosinger, E. E. (2009). Special relativity in reduced power algebras. arXiv:0903.0296v1.

  • Sain, I. (1986). Dynamic logic with nonstandard model theory. Dissertation.

  • Székely, G. (2009). First-order logic investigation of relativity theory with an emphasis on accelerated observers. PhD thesis, Budapest: Eötvös Loránd Univ. http://www.renyi.hu/~turms/phd.pdf.

  • Tarski A. (1959) What is elementary geometry?. In: Henkin L., Suppes P., Tarski A. (eds) The axiomatic method. With special reference togeometry and physics. North-Holland Publishing Co, Amsterdam, pp 16–29

    Google Scholar 

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, P.O. Box 127, Budapest, 1364, Hungary

    Hajnal Andréka, Judit X. Madarász, István Németi & Gergely Székely

Authors
  1. Hajnal Andréka
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  2. Judit X. Madarász
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  3. István Németi
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  4. Gergely Székely
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Correspondence to István Németi.

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Andréka, H., Madarász, J.X., Németi, I. et al. A logic road from special relativity to general relativity. Synthese 186, 633–649 (2012). https://doi.org/10.1007/s11229-011-9914-8

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  • DOI: https://doi.org/10.1007/s11229-011-9914-8

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