Logic Seminar - Pierre Touchard

Date: 
Wed, 20/11/202411:00-13:00
Location: 
Zoom
Zoom link: https://huji.zoom.us/j/86321346360?pwd=GlLwNU2jmFk8bbFrnDkeMo7xADFQOm.1
Title: Automatic definability of henselian valuations
Abstract: In a joint work with Blaise Boissonneau, Franziska Jahnke and Anna De Mase, we study some new questions on the definability of henselian valuation in equicharacteristic 0:
For which field k of characteritic 0, do we have that any henselian valuation with residue field k is definable in the language of ring ?
Similarly, for which ordered abelian group G do we have that any henselian valuation (of equicharacteristic 0) with value group G is definable in the language of ring ?
To give an answer to these questions, we will formulate a simple Ax-Kochen-Ershov principle for the definability of the valuation, which will lead us to interesing questions about ordered abelian groups and linear orders.