Skip to main content
SpringerLink
Log in

Effect test spaces and effect algebras

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The concept of an effect test space, which is equivalent to a D-test space of Dvurečenskij and Pulmannová, is introduced. Connections between effect test space. (E-test space, for short) morphisms, and event-morphisms as well as between algebraic E-test spaces and effect algebras, are studied. Bimorphisms and E-test space tensor products are considered. It is shown that any E-test space admits a unique (up to an isomorphism) universal group and that this group, considered as a test group, determines the E-test space uniquely (up to an isomorphism).

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Dvurečenskij, “Tensor products of difference posets,”Trans. Am. Math. Soc. 347, 1043–1057 (1995).

    Article  Google Scholar 

  2. A. Dvurečenskij and S. Pulmannová, “Difference, posets, effects and quantum measurements,”Int. J. Theor. Phys. 33, 819–850 (1994).

    Article  Google Scholar 

  3. A. Dvurečenskij and S. Pulmannová, “D-test spaces and difference posets,”Rep. Math. Phys. 34, 151–170 (1994).

    Article  MathSciNet  Google Scholar 

  4. D. Foulis and M. K. Bennett, “Effect algebras and unsharp quantum logics,”Found. Phys. 24, 1331–1352 (1994).

    Article  MathSciNet  Google Scholar 

  5. D. Foulis, M. K. Bennet, and R. Greechie, “Test groups and effect algebras,” to appear.

  6. D. Foulis and C. Randall, “Operational statistics I: Basic concepts,”J. Math. Phys. 13, 1667–1675 (1972).

    Article  MathSciNet  Google Scholar 

  7. R. Giuntini and H. Greuling, “Toward a formal, language for unsharp properties,”Found Phys. 19, 931–945 (1989).

    Article  MathSciNet  Google Scholar 

  8. K. Goodearl,Partially Ordered Abelian Groups (American Mathematical Society, Providence, Rhode Island, 1986).

    MATH  Google Scholar 

  9. R. Greechie and D. Foulis, “The transition to effect algebras,”Int. J. Theor. Phys. 34, 1–14 (1995).

    Article  MathSciNet  Google Scholar 

  10. S. Gudder and R. Greechie, “Effect algebra counterexamples,”Math. Slovaca, to appear.

  11. F. Kôpka, “D-posets and fuzzy sets,”Tatra Mountain Math. Publ. 1, 83–87 (1992).

    Google Scholar 

  12. F. Kôpka and F. Chovanec, “D-posets,”Math. Slovaca 44, 21–34 (1994).

    MathSciNet  Google Scholar 

  13. S. Pulmannová and A. Wilee, “Representations ofD-posets,”Int. J. Theor. Phys. 34, 1689–1696 (1995).

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Denver, 80208, Denver, Colorado

    Stanley Gudder

Authors
  1. Stanley Gudder
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gudder, S. Effect test spaces and effect algebras. Found Phys 27, 287–304 (1997). https://doi.org/10.1007/BF02550455

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02550455

Keywords

Search

Navigation