Title: An Introduction to HT-fields
Speaker: Elliot Kaplan - UIUC
Abstract: H-fields were introduced by Aschenbrenner and van den Dries in their study of Hardy fields and fields of transseries. Together with van der Hoeven, they showed that the theory of H-fields has a model companion. In this talk, I will introduce the class of HT-fields, which are real closed H-fields equipped with additional compatible o-minimal structure. Key examples are Hardy fields of o-minimal expansions of the real field and the differential field of logarithmic-exponential transseries expanded by restricted analytic functions. I will conjecture what the model companion for the theory of HT-fields might be, and present some partial progress towards proving this conjecture.
