May 2
Nigel Pynn-Coates,
University of Vienna
D-minimality and more for the asymptotic couple of the field of logarithmic transseries
Associated to certain valued differential fields like transseries and Hardy fields are so-called asymptotic couples, which were introduced by M. Rosenlicht. These are ordered abelian groups equipped with a map induced by the derivation of the valued differential field. I will describe ongoing work with A. Gehret and E. Kaplan on the asymptotic couple of the field of logarithmic transseries, in which we show various notions of smallness coincide. For example, the structure is d-minimal in the sense that every unary definable set with empty interior is a finite union of discrete sets. This enables us to classify all dimension functions on the structure.