Burden of henselian valued fields in the Denef-Pas language

DOI10.1215/00294527-2022-0026arXiv2105.10593MaRDI QIDQ6368265

Publication date: 21 May 2021

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 paper, 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 NTP

_{2}

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."

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Classification theory, stability, and related concepts in model theory (03C45) Non-Archimedean valued fields (12J25) Model theory of fields (12L12) Valued fields (12J10)

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