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Axiomatization of local-global principles for pp-formulas in spaces of orderings

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Abstract.

We use a model theoretic approach to investigate properties of local-global principles for positive primitive formulas in spaces of orderings, such as the existence of bounds and the axiomatizability of local-global principles. As a consequence we obtain various classes of special groups satisfying local-global principles for all positive primitive formulas, and we show that local-global principles are preserved by some natural constructions in special groups.

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Authors and Affiliations

  1. NWF I - Mathematik, Universität Regensburg, 93040, Regensburg, Germany

    V. Astier & M. Tressl

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  1. V. Astier
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  2. M. Tressl
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Correspondence to M. Tressl.

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Mathematics Subject Classification (2000): 11E81, 03C65

Acknowledgement This research was undertaken while both authors were partially suported by the European RTN Network (HPRN-CT-2001-00271) on real algebraic and analytic geometry.

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Astier, V., Tressl, M. Axiomatization of local-global principles for pp-formulas in spaces of orderings. Arch. Math. Logic 44, 77–95 (2005). https://doi.org/10.1007/s00153-004-0236-0

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  • DOI: https://doi.org/10.1007/s00153-004-0236-0

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