Title of the course: Abstract symmetries of first-order structures
Instructor: Prof. Roman Kossak
Institution: City University of New York
Dates: 11-24 September 2016
Level: Graduate, advanced undergraduate
Abstract: I will give an overview of first-order logic, and then proceed with examples of applications showing how model-theoretic
techniques are used to study mathematical structures with particular attention paid to the use of symmetries (automorphisms). The results
I will discuss include a proof of minimality of the ordering of the natural numbers, categoricity of theories with finite domains, and a model
theoretic proof of the infinite Ramsey theorem for pairs.
While the outline above may sound technical, there are no prerequisites for the workshop, other than authentic curiosity. The purpose is not
only to introduce and clarify all necessary mathematical concepts, but also to motivate them by giving their historical and philosophical roots.
There are no prerequisites, but the pace of the workshop will very much depend on how advanced the participants will be. For students with
with no prior exposure to mathematical logic, the emphasis will be on mathematics. For those who already have a grasp of basic concepts of
model theory, there will be more room for historical and philosophical background, and the role of set theory in particular.
Textbook or/and course webpage: I will use my own text “How to Look at Mathematical Structures. On Numbers, Sets, and Symmetry.” (in pdf)