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August 2019 Residue Field Domination in Real Closed Valued Fields
Clifton Ealy, Deirdre Haskell, Jana Maříková
Notre Dame J. Formal Logic 60(3): 333-351 (August 2019). DOI: 10.1215/00294527-2019-0015

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 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. "Residue Field Domination in Real Closed Valued Fields." Notre Dame J. Formal Logic 60 (3) 333 - 351, August 2019. https://doi.org/10.1215/00294527-2019-0015

Information

Received: 21 February 2017; Accepted: 17 October 2017; Published: August 2019
First available in Project Euclid: 2 July 2019

zbMATH: 07120745
MathSciNet: MR3985616
Digital Object Identifier: 10.1215/00294527-2019-0015

Subjects:
Primary: 03C64
Secondary: 03C60, 12J10, 12J25

Rights: Copyright © 2019 University of Notre Dame

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Vol.60 • No. 3 • August 2019
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