Generalised Power Series Determined by Linear Recurrence Relations

Explore a 57-minute lecture from the Fields Institute's Workshop on Tame Geometry, focusing on generalised power series determined by linear recurrence relations. Delve into key concepts such as canonical lifting property, rational functions, linear recurrence sequences, and determined sets. Examine the Main Lemma and its implications for determined fields, including Hahn and Rayner fields. Investigate examples of non-determined Hahn fields and the relationship between F-sequences and the canonical lifting property. Gain insights into the intricate connections between o-minimal, complex analytic, and nonarchimedean methods in tame geometry.

Intro
Notations
Canonical lifting property
Rational functions
Linear recurrence relations
Linear recurrence sequences
Determined sets
Main Lemma
Determined fields
Definition
Determined Hahn fields
Example: non-determined Hahn field
Hahn and Rayner fields
Determined Rayner fields
Task
Rayner fields without the CLP
Hahn fields with the CLP determined by F-sequence
References