Skip to main content

Logic of Space-Time and Relativity Theory

  • Chapter

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Aiello, M. and van Benthem, J. (2002). A modal walk through space. Journal of Applied Non-Classical Logics, 12(3–4):319–363.

    Article  Google Scholar 

  • Alexandrov, A. D. (1974). On foundations of space-time geometry. I. Soviet Math. Dokl., 15:1543–1547.

    Google Scholar 

  • Andréka, H., Madarász, J. X., and Németi, I. (1998–2002). On the logical structure of relativity theories. Technical report, Rényi Institute of Mathematics, Budapest. http://www.math-inst.hu/pub/algebraic-logic/Contents.html.

  • Andréka, H., Madarász, J. X., and Németi, I. (1999). Logical analysis of special relativity theory. In Gerbrandy, J., Marx, M., de Rijke, M., and Venema, Y., editors, Essays dedicated to Johan van Benthem on the occassion of his 50th birthday. Vossiuspers, Amsterdam University Press. CD-ROM, ISBN: 90 5629 104 1, http://www.illc.uva.nl/j50.

    Google Scholar 

  • Andréka, H., Madarász, J. X., and Németi, I. (2004). Logical analysis of relativity theories. In Hendricks, V., Neuhaus, F., Pedersen, S. A., Scheffler, U., and Wansing, H., editors, First-order Logic Revisited, pages 7–36. Logos Verlag, Berlin.

    Google Scholar 

  • Andréka, H., Madarász, J. X., and Németi, I. (2006a). Logical axiomatizations of space-time. Course material on the Internet, http://ftp.math-inst.hu/pub/algebraic-logic/kurzus-2006/kurzus-h-2006.htm.

  • Andréka, H., Madarász, J. X., and Németi, I. (2006b). Logical axiomatizations of space-time. Samples from the literature. In Prékopa, A. and Molnár, E., editors, Non-Euclidean Geometries: János Bolyai Memorial Volume, volume 581 of Mathematics and Its Applications, pages 155–185. Springer Verlag.

    Google Scholar 

  • Andréka, H., Németi, I., and Sain, I. (1982). A complete logic for reasoning about programs via nonstandard model theory, Parts I–II. Theoretical Computer Science, 17:193–212, 259–278.

    Article  Google Scholar 

  • Andréka, H., Németi, I., and Sain, I. (2001). Algebraic Logic. In Gabbay, D. M. and Guenthner, F., editors, Handbook of Philosophical Logic, volume 2, pages 133–247. Kluwer Academic Publishers, second edition. See also http://www.math-inst.hu/pub/algebraic-logic/handbook.pdf.

  • Andréka, H., Németi, I., and Wüthrich, C. (2006c). A twist in the geometry of rotating black holes: seeking the cause of acausality. Manuscript, Budapest and Berne.

    Google Scholar 

  • Ax, J. (1978). The elementary foundations of space-time. Found. Phys., 8(7–8):507–546.

    Article  Google Scholar 

  • Barbour, J. B. (1989). Absolute or relative motion? Cambridge University Press.

    Google Scholar 

  • Basri, S. (1966). A deductive theory of space and time. North-Holland, Amsterdam.

    Google Scholar 

  • Busemann, H. (1967). Time-like spaces, volume 53 of Dissertationes Math. (Rozprawy Math.). Mathematical Istitute of Polish Academy of Sci.

    Google Scholar 

  • Carathéodory, C. (1924). Zur Axiomatik der speziellen Relativitätstheorie. Sitzungsber. phys. math., 14.:12–27.

    Google Scholar 

  • Casini, H. (2002). The logic of causally closed space-time subsets. Classical and Quantum Gravity, 19(24):6389–6404. http://arxiv.org/abs/gr-qc/0205013.

    Article  Google Scholar 

  • Chang, C. C. and Keisler, H. J. (1973). Model theory. North-Holland.

    Google Scholar 

  • d’Inverno, R. (1983). Introducing Einstein’s Relativity. Oxford University Press.

    Google Scholar 

  • Earman, J. (1995). Bangs, crunches, whimpers, and shrieks. Singularities and acausalities in relativistic spacetimes. Oxford University Press, Oxford.

    Google Scholar 

  • Ehlers, J., Pirani, F. A. E., and Shild, A. (1972). The geometry of free fall and light propagation. In General relativity, Papers in Honor of J.L. Synge, pages 63–84. Clarendon Press, Oxford.

    Google Scholar 

  • Einstein, A. (1961). Relativity (The special and the general theory). Wings Books, New York, Avenel, New Jersey.

    Google Scholar 

  • Etesi, G. and Németi, I. (2002). Non-Turing computations via Malament-Hogarth space-times. International Journal of Theoretical Physics, 41(2):341–370.

    Article  Google Scholar 

  • Friedman, H. (2004). On foundational thinking 1, Posting in FOM (Foundations of Mathematics). Archives http://www.cs.nyu.edu.

  • Friedman, M. (1983). Foundations of Space-Time Theories. Relativistic Physics and Philosophy of Science. Princeton University Press.

    Google Scholar 

  • Gödel, K. (1949). An example of a new type of cosmological solutions of Einstein’s field equations of gravitation. Reviews of Modern Physics, 21: 447–450.

    Article  Google Scholar 

  • Goldblatt, R. (1980). Diodorean modality in Minkowski spacetime. Studia Logica, 39:219–236.

    Article  Google Scholar 

  • Goldblatt, R. (1987). Orthogonality and space-time Geometry. Springer-Verlag.

    Google Scholar 

  • Guts, A. K. (1982). Axiomatic relativity theory. Russian Math. Survey, 37(2): 41–89.

    Article  Google Scholar 

  • Hamilton, A. (1997-2001). Falling into a black hole. Internet page, http://casa.colorado.edu/ajsh/schw.shtml.

  • Hawking, S. W. and Ellis, G. F. R. (1973). The large scale structure of space-time. Cambridge University Press.

    Google Scholar 

  • Henkin, L., Monk, J. D., and Tarski, A. (1985). Cylindric Algebras Parts I, II. North-Holland, Amsterdam.

    Google Scholar 

  • Henkin, L., Monk, J. D., Tarski, A., Andréka, H., and Németi, I. (1981). Cylindric Set Algebras, volume 883 of Lecture Notes in Mathematics. Springer-Verlag, Berlin.

    Book  Google Scholar 

  • Hilbert, D. (1899/1977). Grundlagen der Geometrie. Lepzig / B. G. Teubner Verlag, Stuttgart.

    Google Scholar 

  • Hirsch, R. and Hodkinson, I. (2002). Relation algebras by games. North-Holland.

    Google Scholar 

  • Hodges, W. (1993). Model theory. Cambridge University Press.

    Google Scholar 

  • Hogarth, M. L. (2004). Deciding arithmetic using SAD computers. Brit. J. Phil. Sci., 55:681–691.

    Article  Google Scholar 

  • Horváth, R. (2005). An Alexandrov-Zeeman type theorem and relativity theory. Paper for scientific student contest, Eötvös Loránd University, Budapest.

    Google Scholar 

  • Kronheimer, E. H. and Penrose, R. (1967). On the structure of causal spaces. Proc. Camb. Phil. Soc., 63:481–501.

    Article  Google Scholar 

  • Latzer, R. W. (1972). Nondirected light signals and the structure of time. Synthese, 24:236–280.

    Article  Google Scholar 

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

  • Madarász, J. X., Németi, I., and Székely, G. (2006a). First-order logic foundation of relativity theories. In New Logics for the XXIst Century II, Mathematical Problems from Applied Logics, volume 5 of International Mathematical Series. Springer. To appear. philsci-archive.pitt.edu/archive/00002726/.

    Google Scholar 

  • Madarász, J. X., Németi, I., and Székely, G. (2006b). Twin paradox and the logical foundation of relativity theory. Foundations of Physics, 36(5):681–714. http://www.arxiv.org/abs/gr-qc/0504118.

    Article  Google Scholar 

  • Madarász, J. X., Németi, I., and T&odacute;ke, Cs. (2004). On generalizing the logic-approach to space-time towards general relativity: first steps. In Hendricks, V., Neuhaus, F., Pedersen, S. A., Scheffler, U., and Wansing, H., editors, First-order Logic Revisited, pages 225–268. Logos Verlag, Berlin.

    Google Scholar 

  • Makkai, M. (1993). Duality and definability in first order logic. Number 503 in Memoirs of the AMS. AMS.

    Google Scholar 

  • Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1970). Gravitation. Freeman and Co, New York. Twentieth Printing 1997.

    Google Scholar 

  • Mundy, J. (1986). The philosophical content of Minkowski geometry. Britisch J. Philos. Sci., 37(1):25–54.

    Article  Google Scholar 

  • Németi, I. and Andréka, H. (2006). Can general relativistic computers break the Turing barrier? In Beckmann, A. Berger, U. Loewe, B. and Tucker, J. V. editors, Logical Approaches to Computational Barriers, Second Conference on Computability in Europe, CiE 2006, Swansea, UK, July 2006, Proceedings, volume 3988 of Lecture Notes in Computer Science, pages 398–412. Springer-Verlag, Berlin-Heidelberg.

    Google Scholar 

  • Németi, I. and Dávid, Gy. (2006). Relativistic computers and the Turing barrier. Applied Mathematics and Computation, 178:118–142.

    Article  Google Scholar 

  • Nicholls, P., editor (1982). The science in science fiction. Crescent Books, New York.

    Google Scholar 

  • Novikov, I. D. (1998). The river of time. Cambridge University Press.

    Google Scholar 

  • O’Neill, B. (1995). The geometry of Kerr black holes. A K Peters.

    Google Scholar 

  • Pambuccian, V. (2006). Alexandrov-Zeeman type theorems expressed in terms of definability. Aequationes Mathematicae. to appear.

    Google Scholar 

  • Penrose, R. (2004). The road to reality. A complete guide to the laws of the Universe. Jonathan Cape, London.

    Google Scholar 

  • Reichenbach, H. (1969). Axiomatization of the theory of relativity. University of California Press, Berkeley. Translated by M. Reichenbach. Original German edition published in 1924.

    Google Scholar 

  • Rindler, W. (2001). Relativity. Special, General and Cosmological. Oxford University Press.

    Google Scholar 

  • Robb, A. A. (1914). A Theory of Time and Space. Cambridge University Press. Revised edition, Geometry of Time and Space, published in 1936.

    Google Scholar 

  • Sain, I. (1986). Nonstandard dynamic logic. Dissertation for candidate’s degree, Hungarian Academy of Sciences, Budapest. In Hungarian.

    Google Scholar 

  • Schröter, J. (2007). A new formulation of general relativity, Parts I-III. Adv. Theor. Math. Phys., 1:1–70.

    Google Scholar 

  • Schutz, J. W. (1997). Independent axioms for Minkowski space-time. Longoman, London.

    Google Scholar 

  • Schwabhäuser, W., Szmielew, W., and Tarski, A. (1983). Metamathematische Methoden in der Geometrie. Springer-Verlag, Berlin. Hochschul text, viii+482pp.

    Google Scholar 

  • Shehtman, V. and Shapirovsky, I. (2003). Chronological future modality in Minkowski space-time. In Advances in Modal Logic-2002, pages 437–459. King’s College Publications, London.

    Google Scholar 

  • Simpson, S. G., editor (2005). Reverse Mathematics 2001. Lecture Notes in Logic,. Association for Symbolic Logic. pp. x+401.

    Google Scholar 

  • Smolin, L (2001). Three roads to quantum gravity. Basic Books.

    Google Scholar 

  • Suppes, P. (1959). Axioms for relativistic kinematics with or without parity. In Henkin, L., Tarski, A., and Suppes, P., editors, Symposium on the Axiomatic Method with Special Reference to Geometry and Physics, pages 291–307. North-Holland.

    Google Scholar 

  • Suppes, P. (1968). The desirability of formalization in science. The Journal of Philosophy, 27:651–664.

    Article  Google Scholar 

  • Suppes, P. (1972). Some open problems in the philosophy of space and time. Synthese, 24:298–316.

    Article  Google Scholar 

  • Szabó, L. E. (2002). The Problem of Open Future, Determinism in the light of relativity and quantum theory. Typotex, Budapest.

    Google Scholar 

  • Szabó, L. E. (2006). Empiricist studies on special relativity theory. Book manuscript, Budapest.

    Google Scholar 

  • Szczerba, L.W. (1970). Independence of Pasch’s axiom. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 18:491–498.

    Google Scholar 

  • Szekeres, G. (1968). Kinematic geometry: an axiomatic system for Minkowski space-time. Journal of the Australian Mathematical Society, 8:134–160.

    Google Scholar 

  • Szmielew, W. (1974). The role of the Pasch axiom in the foundations of Euclidean Geometry. In Proc. of the Tarski Symp. held in Berkeley in 1971, pages 123–132. Providence, RI.

    Google Scholar 

  • Tarski, A. (1959). What is elementary geometry? In Henkin, L., Tarski, A., and Suppes, P., editors, Symposium on the Axiomatic Method with Special Reference to Geometry and Physics, pages 16–29. North-Holland.

    Google Scholar 

  • Tarski, A. and Givant, S. (1987). A formalization of set theory without variables, volume 41 of AMS Colloquium Publications. Providence, RI.

    Google Scholar 

  • Taylor, E. F. and Wheeler, J. A. (2000). Exploring Black Holes. Introduction to General Relativity. Addison Wesley Longman.

    Google Scholar 

  • Thorne, K. (1994). Black holes and time warps. Einstein’s outrageous legacy. W. W. Norton and Company.

    Google Scholar 

  • van Benthem, J. A. F. K. (1996). Exploring logical dynamics. Studies in Logic, Language and Information. CSLI Publications, Stanford.

    Google Scholar 

  • van Benthem, J. F. A. K. (1982). The logical study of science. Synthese, 51: 431–472.

    Article  Google Scholar 

  • van Benthem, J. F. A. K. (1983). The logic of time, volume 156 of Synthese Library. Reidel Pub. Co., Dordrecht.

    Google Scholar 

  • Wald, R. M. (1984). General Relativity. The University of Chicago Press.

    Google Scholar 

  • Walker, A. G. (1959). Axioms for Cosmology. In Henkin, L., Tarski, A., and Suppes, P., editors, Symposium on the Axiomatic Method with Special Reference to Geometry and Physics, pages 308–321. North-Holland.

    Google Scholar 

  • Winnie, J. A. (1977). The causal theory of space-time. In Earman, J. S., Glymour, C. N., and Stachel, J. J., editors, Foundations of space-time Theories, pages 134–205. University of Minnesota Press.

    Google Scholar 

  • Wüthrich, C. (1999). On time machines in Kerr-Newman spacetime. Master’s thesis, University of Berne.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer

About this chapter

Cite this chapter

Andréka, H., Madarász, J., 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, Dordrecht. https://doi.org/10.1007/978-1-4020-5587-4_11

Download citation

Publish with us

Policies and ethics