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Strongly dependent ordered abelian groups and Henselian fields

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Abstract

Strongly dependent ordered abelian groups have finite dp-rank. They are precisely those groups with finite spines and |{p prime : [G:pG]=∞}|<∞. We apply this to show that if K is a strongly dependent field, then (K, v) is strongly dependent for any Henselian valuation v.

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Author information

Authors and Affiliations

  1. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem, 91904, Israel

    Yatir Halevi

  2. Department of mathematics, Ben Gurion University of the Negev, Be’er Sheva, 84105, Israel

    Assaf Hasson

Authors
  1. Yatir Halevi
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  2. Assaf Hasson
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Corresponding author

Correspondence to Yatir Halevi.

Additional information

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 291111.

Supported by ISF grant No. 181/16.

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Halevi, Y., Hasson, A. Strongly dependent ordered abelian groups and Henselian fields. Isr. J. Math. 232, 719–758 (2019). https://doi.org/10.1007/s11856-019-1885-3

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  • DOI: https://doi.org/10.1007/s11856-019-1885-3

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