Set Theoretical Forcing in Quantum Mechanics and AdS/CFT Correspondence

International Journal of Theoretical Physics

Volumn 42, Issue 5, 2003, Pages 921-935

  Król, Jerzy ^a  

^a UNIVERSITY OF SILESIA   (Poland)

Author keywords

Boolean models of ZFC; Exotic R4; Forcing; Quantum mechanics

Indexed keywords

EID: 0041355339     PISSN: 00207748     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025410204119     Document Type: Conference Paper

References (48)

1. Albeverio, S., Fenstad, J. E., Høegh-Krohn, R., and Lindstrøm, T. (1986). Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Academic Press, Orlando, FL.
2. Asselmeyer, T. (1997). Generation of source terms in general relativity by differential structures. Classical and Quantum Gravity 14, 749-758.
3. Bell, J. L. (1983). Orthologic, forcing, and the manifestation of attributes, In Proceedings of the Southest Asian Conference on Logic, C. T. Chong and M. J. Wicks, eds., Elsevier, North-Holland, The Netherlands.
4. Bell J. L. (1985a). Boolean-Valued Models and Independence Proofs in Set Theory, 2nd edn., Oxford University Press, Oxford.
5. Bell J. L. (1985b). Orthospaces and quantum logic. Foundations of Physics 15(12), 1179-1202.
6. Benioff P. (2001). Preprint quant-ph/0103078, quant-ph/0106153.
7. 4's, Journal of Differential Geometry 43, 458-504.
8. Blass A. (1977). End extensions, conservative extensions, and the Rudin Frolik ordering, Transactions of the American Mathematical Society 225, 325-340.
9. Brans C. H. (1994). Journal of Mathematical Physics 35, 5494.
10. Cohen P. J. (1966). Set Theory and the Continuum Hypothesis, Benjamin, New York.
11. Dalla Chiara M., Giuntini R. (2001). Quantum logics. In Handbook of Philosophical Logic, D. Gabbay, ed., Kluwer, Dordrecht, The Netherlands.
12. Fearins J. D. (2002). A Physical Quantum Model in a Smooth Topos. (quant-ph/0202079)
13. Freedman M. H. (1982). the topology of four-dimensional manifolds, Journal of Differential Geometry 17, 357-453.
14. Gompf R. E., Stipsicz A. I. (1999). An Introduction to 4-Manifolds and Kirby Calculus, American Mathematical Society, Providence, RI.
15. Guts A., Zvyagitser A. (1999, 2001). Preprint physics/9909016, gr-qc/0001076.
16. Isham C., Butterfield J. (1999). International Journal of Theoretical Physics 38, 827.
17. Jech T. (1978). Set Theory, Academic Press, New York.
18. Jech T. (1984). Abstract theory of Abelian operator algebras: An application of forcing, Transactions of the American Mathematical Society 289(1), 133-162.
19. Johnstone P. T. (1977). Topos Theory, Academic Press, London.
20. Kamo V. (1981). Nonstandard natural number system and nonstandard models, Journal of Symbolic Logic 46, 365-376.
21. Keisler H. J., Chang C. C. (1990). Model Theory, 3rd edn., North-Holland, Amsterdam.
22. Kirby R. C. (1989). The topology of 4-manifolds. In Lectures Notes in Mathematics, Vol. 1374, Springer-Verlag, Berlin.
23. Kochen S., Specker V. (1967). Journal of Mathematics and Mechanics 17(1).
24. Kock A. (1981). Synthetic Differential Geometry, London Mathematical Society, Lecture Notes, Series 51, Cambridge University Press, Cambridge, UK.
25. Król J. (2001). Formal languages and model theoretic perspectives in physics, Acta Physica Polonica B 32(11), 3855-3871.
26. Król J. (2003). Background independence in quantum gravity and forcing constructions. Foundations of Physics, to appear.
27. Loeb P. A. (1982). Measure spaces in nonstandard models underlying standard stochastic processes. In Proceedings of the International Congress of Mathematics Warsaw, PWN, North Holland, Vol. 1, pp. 323-336.
28. MacLane S., Moerdijk I. (1992). Sheaves in Geometry and Logic: A First Introduction to Topos Theory, Springer-Verlag, Berline.
29. Maldacena J. (1997). Advances in Theoretical Mathematical Physics 2, (231). Preprint hep-th/9711200
30. Mansfield R. (1971) The theory of Boolean ultrapowers, Annals of Mathematical Logic 2, 297-323.
31. Moerdijk I., Reyes G. E. (1991). Models for Smooth Infinitesimal Analysis, Springer-Verlag, New York.
32. Murakami M. (1999). Standardization principle of nonstandard universes, Journal of the Symbolic Logic 64(4), 1645-1655.
33. Ozawa M. (1994). Forcing in nonstandard analysis, Annals of Pure and Applied Logic 68, 263-297.
34. Polchinski J., Strassler M. J. (2000). The String Dual of a Confining Four-Dimensional Gauge Theory. (hep-th/0003136)
35. Raptis I. (2001). Preasheves, Sheaves and Their Topoi in Quamtum Gravity and Quantum Logic. (gr-qc/0110064)
36. Robinson A. (1966). Non-standard analysis. In Studies in Logic and the Foundations of Mathematics, North Holland, Amsterdam.
37. Robinson A., Barwise J. (1971). Completing theories by forcing, Annals of Mathematical Logic 2, 119-142.
38. Robinson, A. (1979). Topics in Non-Archimedean Mathematics (Collected Papers), pp. 99-112, North North Holland, Amsterdam.
39. Scott D. (1969). Boolean Models and Nonstandard Analysis. In Applications of Model Theory to Algebra, Analysis, and Probobility, pp. 87-92, W. A. J. Luxenburg, ed., Holt, Reinehart & Winston, New York.
40. Sikorski R., Rasiowa H., (1963). The Mathematics of Metamathematics, PWN, Warszawa.
41. 4's with few symmetries, International Journal of Modern Physics D 10, 311.
42. Takeuti G. (1978). Two Applications of Logic to Mathematics, Mathematical Society of Japan 13, Kano Memorial Lectures 3.
43. Takeuti G. (1979). Boolean valued analysis: Applications of sheaves. In Lecutres Notes in Mathematics, Vol. 753, Fourman, Mulvey, and Scott, eds, Springer-Verlog, Heildelberg, p. 714.
44. Takeuti G. (1983). Quantum set theory. In Current Issues in Quantum Logic, E. Beltrametti and B. C. van Frassen, eds., Plenum, New York p. 303.
45. von Neuman J., Birghoff G. (1936). Annals of Mathematics 37, 823.
46. Vopenka P. (1965). The limits of sheaves and applications on constructions of models, Bulletin de l'Academie Polonaise des Sciences 13, 189-192.
47. Witten E. (1998). Anti-de Sitter space and holography, Advances in Theoretical and Mathematical Physics 2, 231. (hep-th/9802150)
48. Witten E., Klebanov I. R. (1999). AdS/CFT correspondence and symmetry breaking, Nuclear Physics B 556, 89-114.