Collection Model Theory and Valued Fields
Organizer(s)
Date(s)
05/03/2018
- 09/03/2018
Toward an imaginary Ax-Kochen-Ershov principle.
All imaginaries that have been classified in Henselian fields (possibly with operators) have been shown to be geometric in the sense of Haskell-Hrushovski-Macpherson. In general, imaginaries in the residue field and value group also need to be taken into account and one could hope that, in the spirit of the Ax-Kochen-Ershov principle, this is all one needs to add, on top of the geometric imaginaries, to get elimination of imaginaries in equicharacteristic zero Henselian fields (possibly with operators). This is, in fact, not the case but I will present recent results giving convincing evidence that this statement does hold if one takes into account the obvious obstructions. I will then apply these results to the asymptotic theory of ACVFp,p with the Frobenius. This is joint work with Martin Hils
