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Local-global properties of positive primitive formulas in the theory of spaces of orderings

Published online by Cambridge University Press:  12 March 2014

M. Marshall*
Affiliation:
University of Saskatchewan, Department of Mathematics & Statistics, Saskatoon, Sk, S7N 5E6, Canada, E-mail: marshall@snoopy.usask.ca

Abstract

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Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2006

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References

REFERENCES

[1]Andradas, C., Bröcker, L., and Ruiz, J., Constructible Sets in Real Geometry, Ergebnisse der Mathematik, vol. 33, Springer, 1996.CrossRefGoogle Scholar
[2]Astier, V. and Tressl, M., Axiomatization of local-global principles for pp formulas in spaces of orderings, 2004, preprint.CrossRefGoogle Scholar
[3]Bochnak, J., Coste, M., and Roy, M.-F., Real Algebraic Geometry, Ergebnisse der Mathematik, vol. 36, Springer, 1998.CrossRefGoogle Scholar
[4]Bröcker, L., Spaces of orderings and semi-algebraic sets, Quadratic and Hermitian Forms, Conference Proceedings of the Canadian Mathematical Society, 1984, pp. 231248.Google Scholar
[5[Craven, T., Witt rings and orderings on skew fields, Journal of Algebra, vol. 77 (1982), pp. 7496.CrossRefGoogle Scholar
[6]Craven, T., Orderings, valuations and Hermitian forms over skewfields, Proceedings of the Symposia on Pure Mathematics, vol. 58, 1995, pp. 149158.Google Scholar
[7]Dickmann, M., Marshall, M., and Miraglia, F., Lattice ordered reduced special groups, Annals of Pure and Applied Logic, vol. 132 (2005), pp. 2749.CrossRefGoogle Scholar
[8]Dickmann, M. and Miraglia, F., Special groups: Boolean-theoretic methods in the theory of quadratic forms, Memoirs of the AMS, vol. 145 (2000), no. 689.CrossRefGoogle Scholar
[9]Gładki, P. and Marshall, M., The pp conjecture for spaces of orderings of rational conics, to appear.Google Scholar
[10]Kalhoff, F., Orderings, algebras and projective planes, Expositiones Mathematicae, vol. 13 (1995), pp. 338.Google Scholar
[11]Knebusch, M., On the local theory of signatures and reduced quadratic forms, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 51 (1981), pp. 141195.CrossRefGoogle Scholar
[12]Lam, T.-Y., Orderings, valuations and quadratic forms, Regional Conference Series in Mathematics, vol. 52, American Mathematical Society, 1983.CrossRefGoogle Scholar
[13]Leung, K. H., Marshall, M., and Zhang, Y., The real spectrum of a noncommutative ring, Journal of Algebra, vol. 98 (1997), pp. 412427.CrossRefGoogle Scholar
[14]Marshall, M., Spaces of orderings IV, Canadian Journal of Mathematics, vol. 32 (1980), pp. 603627.CrossRefGoogle Scholar
[15]Marshall, M., Spaces of orderings: Systems of quadratic forms, local structure and saturation, Communications in Algebra, vol. 12 (1984), pp. 723743.CrossRefGoogle Scholar
[16]Marshall, M., Spaces of orderings and abstract real spectra, Lecture Notes in Mathematics, vol. 1636, Springer, 1996.CrossRefGoogle Scholar
[17]Marshall, M., *-orderings on a ring with involution, Communications in Algebra, vol. 28 (2000), pp. 11571173.CrossRefGoogle Scholar
[18]Marshall, M., Open questions in the theory of spaces of orderings, this Journal, vol. 67 (2002), pp. 341352.Google Scholar
[19]Marshall, M., A note concerning the curve x2 + y2 = 3, unpublished note, 2005.Google Scholar
[20]Walter, L., Quadratic forms, orderings, and quaternion algebras over rings with many units, Master Thesis, University of Saskatchewan, 1988.Google Scholar