Logic Seminar: Lou van den Dries (UIUC)

Title: An extension result for motivic measures 


Abstract: Let K be a real closed field extension of the field $\R$ of real numbers, with $\R$ as a distinguished subset of K, named by a unary predicate. The Euler characteristic of semialgebraic sets in $\R^n$, $n=0,1,2,\dots$, extends nicely to the subsets of the K^n that are internal to $\R$. This is a special case of a general extension result for motivic measures. The latter gives answers to questions left open in the paper ``Dimension in the realm of transseries’' by Aschenbrenner, van der Hoeven, and myself.