Abstract: 

In this talk we will introduce the study of fragments of NIP formulas in some theories of valued fields. In particular, building on a celebrated theorem of Johnson that states that any NIP valued field of positive characteristic is necessarily henselian, we show that the same is true when restricting the family of NIP formulas to the existential fragment. If time allows, we will show how the proof works for finer fragments (positive existential, with a given number of existential quantifiers) when the valued field in question is type-definable in some structure where such formulas are NIP.

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