 
Summary: UIC Model Theory Seminar, September 12, 2006
Model theory of valued difference fields
Salih Azgin
University of Illinois at UrbanaChampaign
A classical result by AxKochen and Ershov provides a very good un
derstanding of the model theory of finitely ramified henselian valued
fields. "Model Theory of Frobenius on Witt Vectors" (preprint, Belair
MacintyreScanlon) pursues a similar goal in the context of valued dif
ference fields, i.e., valued fields with a distinguished automorphism.
Our goal is to prove an analogue of the main result of the BMS
paper in equal characteristic p > 0. We shall start by considering val
ued difference fields in equal characteristic zero, where the interaction
between the valuation and the distinguished automorphism is different
than that of the BMS context. Even though this seems irrelevent to the
question at hand, it provides good insight to the model theory valued
fields and valued difference fields in equal characteristic p > 0.
