1. The existential theory of equicharacteristic henselian valued fields
- Author
-
Sylvy Anscombe and Arno Fehm
- Subjects
Model theory ,Pure mathematics ,G110 ,diophantine equations ,12J10 ,Field (mathematics) ,0102 computer and information sciences ,Commutative Algebra (math.AC) ,01 natural sciences ,Existentialism ,Corollary ,Residue field ,03C60, 12L12, 12J10, 11U05, 12L05 ,Computer Science::Logic in Computer Science ,FOS: Mathematics ,henselian valued fields ,0101 mathematics ,03C60 ,Mathematics ,12L05 ,Algebra and Number Theory ,Mathematics::Commutative Algebra ,Group (mathematics) ,Diophantine equation ,010102 general mathematics ,decidability ,11U05 ,Mathematics - Logic ,Mathematics - Commutative Algebra ,Decidability ,Mathematics::Logic ,010201 computation theory & mathematics ,model theory ,12L12 ,Logic (math.LO) ,Computer Science::Formal Languages and Automata Theory - Abstract
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 $\mathbb{F}_{q}((t))$.
- Published
- 2016