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arXiv · 1702.06504

Residue field domination in real closed valued fields

Clifton Ealy·Deirdre Haskell·Jana Maříková
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Abstract

We define a notion of residue field domination for valued fields which generalizes stable domination in algebraically closed valued fields. We prove that a real closed valued field is dominated by the sorts internal to the residue field, over the value group, both in the pure field sort and in the geometric sorts. These results characterize forking and þ-forking in real closed valued fields (and also algebraically closed valued fields). We lay some groundwork for extending these results to a power-bounded $T$-convex theory.

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Clifton Ealy, Deirdre Haskell, Jana Maříková. 2017-03-16. Residue field domination in real closed valued fields. https://doi.org/10.1215/00294527-2019-0015

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