Skip to main content
SpringerLink
Log in

On some sheaves of special groups

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract

Using sheaves of special groups, we show that a general local-global principle holds for every reduced special group whose associated space of orderings only has a finite number of accumulation points. We also compute the behaviour of the Boolean hull functor applied to sheaves of special groups.

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.

Similar content being viewed by others

References

  1. Astier V. and Tressl M. (2005). Axiomatization of local-global principles for pp-formulas in spaces of orderings. Arch. Math. Logic 44(1): 77–95

    Article  MATH  MathSciNet  Google Scholar 

  2. Dickmann, M.: Anneaux de witt abstraits et groupes spéciaux. In: Séminaire de Structures Algébriques Ordonnées, vol. 42, Paris VII-CNRS, Logique, Prépublications (1993)

  3. Dickmann M.A. and Miraglia F. (2000). Special groups: Boolean-theoretic methods in the theory of quadratic forms (With appendixes A and B by Dickmann and A. Petrovich). Mem. Am. Math. Soc. 145(689): xvi+247

    MathSciNet  Google Scholar 

  4. Ellerman D.P. (1974). Sheaves of structures and generalized ultraproducts. Ann. Math. Logic 7: 163–195

    Article  MATH  MathSciNet  Google Scholar 

  5. Gladki, P., Marshall, M.: The pp conjecture for spaces of orderings of rational conics (to appear)

  6. Hurewicz W. and Wallman H. (1941). Dimension Theory. Princeton Mathematical Series vol. 4.. Princeton University Press, Princeton

    Google Scholar 

  7. Lira de Lima, A.: Les groupes spéciaux, aspects algébriques et combinatoires de la théorie des espaces d’ordres abstraits. Ph.D. thesis, University Paris 7 (1997)

  8. Marshall M. (1980). Abstract Witt rings, Queen’s Papers in Pure and Applied Mathematics, vol. 57. Queen’s University, Kingston

    Google Scholar 

  9. Marshall, M.A.: Spaces of orderings and abstract real spectra, Lecture Notes in Mathematics, vol. 1636. Springer, Berlin (1996)

  10. Marshall M.A. (2002). Open questions in the theory of spaces of orderings. J. Symbolic Logic 67(1): 341–352

    MATH  MathSciNet  Google Scholar 

  11. Pierce, R.S.: Modules over commutative regular rings. Memoirs of the American Mathematical Society, No. 70. American Mathematical Society, Providence (1967)

Download references

Author information

Authors and Affiliations

  1. FB Mathematik und Statistik, D203, Universität Konstanz, 78457, Konstanz, Germany

    Vincent Astier

Authors
  1. Vincent Astier
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vincent Astier.

Additional information

The research leading to this note was carried out with the partial support of the European RTN Networks HPRN-CT-2002-00287 “Algebraic K-Theory, Linear Algebraic Groups and Related Structures”, and HPRN-CT-2001-00271 “Real Algebraic and Analytic Geometry”

Rights and permissions

Reprints and permissions

About this article

Cite this article

Astier, V. On some sheaves of special groups. Arch. Math. Logic 46, 481–488 (2007). https://doi.org/10.1007/s00153-007-0051-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-007-0051-5

Keywords

Mathematics Subject Classification (2000)

Search

Navigation