Both Hardy fields and fields of transseries provide interesting models of valued fields with an additional ordered differential structure. In our talk we show that the field of differentially algebraic transseries over the real numbers can be embedded in a Hardy field. The proof relies on the concept of a “transserial Hardy field”, which both carries the structure of a Hardy field and of a differential subfield of the field of transseries. We will associate analytic meanings to transseries using a technique of iterated integrals. We will also indicate ongoing generalizations to H-fields in collaboration with Matthias Aschenbrenner and Lou van den Dries.

Occasion: Conference on Mathematical Logic 2018, Niterói, Brasil, august 11, 2018

Documents: slideshow, TeXmacs source