London Logic Seminar – Gabriel Ng

Title: Differentially Henselian Fields

Abstract: We say that a valued-differential field is differentially henselian if it is henselian as a pure valued field and satisfies a certain ‘differential lifting’ property. We will look at these fields in the context of differential largeness, which is a notion for differential fields which  eneralises ‘large’ or ‘ample’ fields. In this talk, we will begin with a brief review of the background on henselian valued fields and differential  argeness; then we will exhibit a number of results that can be lifted from henselian fields to differentially henselian fields via an embedding  theorem, including various forms of the Ax-Kochen-Ershov principle, and stable embeddedness results.

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