November 2022 Burden of Henselian Valued Fields in the Denef–Pas Language
Peter Sinclair
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Notre Dame J. Formal Logic 63(4): 463-480 (November 2022). DOI: 10.1215/00294527-2022-0026

Abstract

Motivated by the Ax–Kochen/Ershov principle, a large number of questions about Henselian valued fields have been shown to reduce to analogous questions about the value group and residue field. In this article, we investigate the burden of Henselian valued fields in the three-sorted Denef–Pas language. If T is a theory of Henselian valued fields admitting relative quantifier elimination (in any characteristic), we show that the burden of T is equal to the sum of the burdens of its value group and residue field. As a consequence, T is NTP2 if and only if its residue field and value group are; the same is true for the statements “T is strong” and “T has finite burden.”

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Peter Sinclair. "Burden of Henselian Valued Fields in the Denef–Pas Language." Notre Dame J. Formal Logic 63 (4) 463 - 480, November 2022. https://doi.org/10.1215/00294527-2022-0026

Information

Received: 21 May 2021; Accepted: 27 July 2022; Published: November 2022
First available in Project Euclid: 16 December 2022

MathSciNet: MR4522322
zbMATH: 07634478
Digital Object Identifier: 10.1215/00294527-2022-0026

Subjects:
Primary: 03C45 , 12J10
Secondary: 03C60 , 12J25

Keywords: burden , Denef–Pas language , dp-rank , Henselian , NTP2 , valued fields

Rights: Copyright © 2022 University of Notre Dame

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Vol.63 • No. 4 • November 2022
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