Summary: UIC Model Theory Seminar, September 12, 2006
Model theory of valued difference fields
University of Illinois at Urbana-Champaign
A classical result by Ax-Kochen 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-
Macintyre-Scanlon) 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.