Anna De Mase

This project concerns Model theory, a branch of Mathematical logic that has many connections with algebra, number theory, and diophantine geometry. The attention is focused on Hahn fields of power series and their groups of valuation preserving automorphisms. The first goal is constructing a "good" embedding of a equicha racteristic valued field into a Hahn field to obtain subfields of power series with some nice properties concerning their automorphisms. This will allow us to construct subfields of a Hahn field for which an explicit description of their group of valuation-preserving automorphisms exists. The second goal is to analyze an analogous problem in the case of mixed characteristic valued fields. Thus, we consider a mixed characteristic valued field with an embedding into a field of twisted power series, i.e. power series where the multiplication is defined by adding an extra factor, to preserve the positive characteristic of the residue field.