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Valued difference fields and NTP2

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Abstract

We show that the theory of the non-standard Frobenius automorphism, acting on an algebraically closed valued field of equal characteristic 0, is NTP2. More generally, in the contractive as well as in the isometric case, we prove that a σ-Henselian valued difference field of equicharacteristic 0 is NTP2, provided both the residue difference field and the value group (as an ordered difference group) are NTP2.

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Authors and Affiliations

  1. Einstein Institute of Mathematics Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel

    Artem Chernikov

  2. Institut de Mathématiques de Jussieu (UMR 7586 du CNRS), Université Paris Diderot Paris 7, UFR de Mathématiques - case 7012, 75205, Paris Cedex 13, France

    Martin Hils

  3. École Normale Supérieure, Département de mathématiques et applications, UMR 8553 du CNRS, 45 rue d’Ulm, 75230, Paris Cedex 05, France

    Martin Hils

Authors
  1. Artem Chernikov
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  2. Martin Hils
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Correspondence to Artem Chernikov.

Additional information

The first author was supported by the Marie Curie Initial Training Network in Mathematical Logic - MALOA - From MAthematical LOgic to Applications, PITN-GA-2009-238381.

The second author was partially funded by the Agence Nationale de Recherche [MODIG, Projet ANR-09-BLAN-0047].

A substantial part of the research was carried out during the program’ Model Theory and Applications’ at the Max Planck Institut für Mathematik in Bonn. The second author would like to thank the MPIM for its hospitality and support.

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Chernikov, A., Hils, M. Valued difference fields and NTP2 . Isr. J. Math. 204, 299–327 (2014). https://doi.org/10.1007/s11856-014-1094-z

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  • DOI: https://doi.org/10.1007/s11856-014-1094-z

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