Surreal Ordered Exponential Fields

Explore the fascinating world of surreal ordered exponential fields in this 59-minute seminar presented by Elliot Kaplan from Fields Institute/McMaster University. Delve into the intricacies of surreal numbers, their tree structure, and exponential properties. Investigate Hahn fields, initial subfields of No, and exponential subfields. Examine the concept of transseries fields and their role in modeling real exponentiation. Gain insights into elementary extensions of R and discover partial answers to complex mathematical questions. This thought-provoking talk, part of the 2021-2022 Geometry and Model Theory Seminar series, offers a deep dive into advanced mathematical concepts for those interested in surreal number theory and its applications.

Intro
The surreal numbers
The surreal number tree
Surreal exponentiation
The motivating question
Hahn fields
Initial subfields of No
More on initial subfields
Exponential sublields of No
An initial guess
What goes right?
What's missing?
Transseries fields
Elementary extensions of R..
Models of real exponentiation
Partial answers
Transserial embeddings