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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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