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# The existential theory of equicharacteristic henselian valued fields

Type of Publication: | Preprint |

Author: | Anscombe, Will; Fehm, Arno |

Year of publication: | 2015 |

ArXiv-ID: | arXiv:1501.04522 |

Summary: |
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 F
_{q}((t)). |

Subject (DDC): | 510 Mathematics |

Bibliography of Konstanz: | Yes |

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ANSCOMBE, Will, Arno FEHM, 2015. The existential theory of equicharacteristic henselian valued fields

@unpublished{Anscombe2015exist-31209, title={The existential theory of equicharacteristic henselian valued fields}, year={2015}, author={Anscombe, Will and Fehm, Arno} }