Submission date: 11 June 2017

Abstract:

Strongly dependent ordered abelian groups have finite dp-rank. They are precisely those groups with finite spines and |{p prime : [G:pG]= ∞ }|<∞. We conclude that, if K is a strongly dependent field, then (K,v) is strongly dependent for any henselian valuation v and the value group and residue field are stably embedded as pure structures.

Mathematics Subject Classification:

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Full text arXiv 1706.03376: pdf, ps.