Asymptotic and Multidimensional Asymptotic Classes of Finite Structures

Explore the intricacies of asymptotic and multidimensional asymptotic classes of finite structures in this 51-minute Association of Symbolic Logic Invited Address given by Charles Steinhorn from Vassar College at the Joint Mathematics Meetings. Delve into the motivation and inspiration behind the topic, examine the beautiful theorem, and investigate n-dimensional asymptotic classes. Learn about one-variable criterion, one-dimensional asymptotic classes, and smoothly approximating structures. Discover a-definable regularity lemma, ultraproducts of asymptotic classes, measurable setters, and measurable structures. Engage with questions on multidimensional asymptotic classes, measuring semirings, and generalized measurable structures to gain a comprehensive understanding of this advanced mathematical concept.

Introduction
Outline
Motivation
Inspiration
The beautiful theorem
Ndimensional asymptotic classes
One variable criterion
Onedimensional asymptotic classes
Smoothly approximating structures
Adefinable regularity lemma
Ultraproducts of asymptotic classes
Measurable setters
Measurable structures
Questions
Multidimensional asymptotic classes
Measuring semirings
Generalized measurable structures