August 11 (Wednesday) 2021 16:00 - 18:00,Building 110, Room N103

▶Speaker: Junguk Lee (KAIST)
▶Title : An introduction to the AKE-principle
▶Abstract:
In model theory of valued fields, one of fundamental results is the AKE-principle proved by Ax-Kochen and independently Ershov. It says that given two unramified Henselian valued fields of equal characteristic zero, two valued fields are elementary equivalent if and only if their residue fields and value groups are elementary equivalent. The AKE principle induces the transfer principle for first order sentence between unramified local fields of characteristic (0,p) and (p,p) and using the transfer principle, Ax and Kochen proved the Artin conjecture on the Diophantine dimension for unramified local fields of characteristic (0,p), which led them to win Cole prize.
In the first part of the talk, I will briefly recall basic model theory, and introduce the AKE-principle and its several applications. In the second part, I will introduce my contributions to the AKE-principle for finitely ramified case, based on my work and joint work with Wan Lee.


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