Skip to main content
Log in

Direct Limits of Effect Algebras

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In this paper, we prove that direct limits exist in the category of effect algebrasand effect algebra-morphisms. Then, as a consequence, we obtain similar knownresults for the categories of orthomodular posets and orthomodular lattices.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. E. Beltrametti and G. Cassinelli, The Logic of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts, 1981.

    Google Scholar 

  2. G. Birkhoff and J. von Neumann, The logic of quantum mechanics, Ann. Math. 37 (1936) 823-843.

    Google Scholar 

  3. T. Blyth and M. Janowitz, Residuation Theory, Pergamon Press, Oxford, 1972.

    Google Scholar 

  4. J. Dacey, Orthomodular spaces, Ph.D. Thesis, University of Massachusetts, Amherst, 1968.

    Google Scholar 

  5. H. Fischer and G. Rüttimann, Limits of manuals and logics, in Mathematical Foundation of Quantum Theory, A. Marlow, ed., Academic Press, New York, 1978, pp. 127-152.

    Google Scholar 

  6. D. Foulis and M. K. Bennett, Effect algebras and unsharp quantum logics, Found. Phys. 24 (1994) 1325-1346.

    Google Scholar 

  7. D. Foulis, R. J. Greechie, and G. Rüttimann, Filters and supports, Int. J. Theor. Phys. 31 (1992) 789-807.

    Google Scholar 

  8. D. Foulis and C. Randall, Operational statistics I: Basic concepts, J. Math. Phys. 13 (1972) 1167-1175.

    Google Scholar 

  9. S. Gudder, Stochastic Methods in Quantum Mechanics, North-Holland, New York, 1979.

    Google Scholar 

  10. S. Gudder, Quantum Probability, Academic Press, New York, 1988.

    Google Scholar 

  11. E. Habil, Morphisms and pasting of orthoalgebras, Math. Slovaca 47 (1997) 405-416.

    Google Scholar 

  12. E. Habil, Orthosummable orthoalgebras, Int. J. Theor. Phys. 33 (1994) 1957-1984.

    Google Scholar 

  13. G. Kalmbach, Orthomodular Lattices, Academic Press, New York, 1983.

    Google Scholar 

  14. F. Kôpka and F. Chovanec, D-posets, Math. Slovaca 44 (1994) 21-34.

    Google Scholar 

  15. G. Mackey, The Mathematical Foundations of Quantum Mechanics, Benjamin, New York, 1963.

    Google Scholar 

  16. C. Piron, Foundations of Quantum Physics Benjamin, New York, 1976.

    Google Scholar 

  17. P. Pták and S. Pulmannová, Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht,1991.

    Google Scholar 

  18. S. Pulmannová, Difference posets and the histories approach to quantum theories, Int. J. Theor. Phys. 34 (1995) 189-210.

    Google Scholar 

  19. C. Randall and D. Foulis, Operational statistics II: Manuals of operations and their logics, J. Math. Phys. 14 (1973) 1472-1480.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Habil, E.D. Direct Limits of Effect Algebras. International Journal of Theoretical Physics 39, 711–720 (2000). https://doi.org/10.1023/A:1003602224196

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1003602224196

Keywords

Navigation