Algebra & Number Theory
- Algebra Number Theory
- Volume 10, Number 3 (2016), 665-683.
The existential theory of equicharacteristic henselian valued fields
We study the existential (and parts of the universal-existential) theory of equicharacteristic henselian valued fields. We prove, among other things, an existential Ax–Kochen–Ershov principle, which roughly says that the existential theory of an equicharacteristic henselian valued field (of arbitrary characteristic) is determined by the existential theory of the residue field; in particular, it is independent of the value group. As an immediate corollary, we get an unconditional proof of the decidability of the existential theory of .
Algebra Number Theory, Volume 10, Number 3 (2016), 665-683.
Received: 18 September 2015
Revised: 9 February 2016
Accepted: 15 March 2016
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03C60: Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]
Secondary: 12L12: Model theory [See also 03C60] 12J10: Valued fields 11U05: Decidability [See also 03B25] 12L05: Decidability [See also 03B25]
Anscombe, Sylvy; Fehm, Arno. The existential theory of equicharacteristic henselian valued fields. Algebra Number Theory 10 (2016), no. 3, 665--683. doi:10.2140/ant.2016.10.665. https://projecteuclid.org/euclid.ant/1510842499