Speaker:
Piotr Błaszkiewicz (University of Szczecin)

Title:
Krasner’s valued hyperfields and amc-structures

Abstract:
The aim of the talk is to relate the amc-structures and valued 
hyperfields. In 1994 Franz-Viktor Kuhlmann introduced amc-structures 
in the work "Quantifier elimination for henselian fields relative to 
additive and multiplicative congruences" for the problem of quantifier 
elimination for henselian valued fields. Valued hyperfields, on the 
other hand, were introduced in 1957 by Marc Krasner in "Approximation 
des corps valués complets de caractéristique p not= 0 par ceux de 
caractéristique 0", but in the context of model theory of valued 
fields were first used in 2020 by Junguk Lee in the paper "Hyperfields, 
truncated DVRs and valued fields". This latter work gave us the 
motivation to take a look at valued hyperfields in the context of 
quantifier elimination in valued fields, and hence, their relation 
to amc-structures.