## Notre Dame Journal of Formal Logic

### Residue Field Domination in Real Closed Valued Fields

#### 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.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 60, Number 3 (2019), 333-351.

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

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1562033115

Digital Object Identifier
doi:10.1215/00294527-2019-0015

Mathematical Reviews number (MathSciNet)
MR3985616

#### Citation

Ealy, Clifton; Haskell, Deirdre; Maříková, Jana. Residue Field Domination in Real Closed Valued Fields. Notre Dame J. Formal Logic 60 (2019), no. 3, 333--351. doi:10.1215/00294527-2019-0015. https://projecteuclid.org/euclid.ndjfl/1562033115

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