The course covers the fundamentals of computable structure theory with a focus on noncomputable structures. The learning outcomes include understanding the basics of categoricity, computability, and effective categoricity in computable structures. Students will learn about computable categoricity, noncomputable fields, and the isomorphism types of subfields. The teaching method involves theoretical explanations, hands-on examples, and the presentation of theorems. This course is intended for individuals interested in advanced topics in mathematical logic and computability theory.
Overview
Syllabus
Intro
An opening thought
Basics of categoricity
Computability and categoricity
Trying to define effective categoricity First stab at computable categoricity
An alternative path
Is this really much different? The definition of computable categoricity for a computable structure
Chronology
Two hands-on examples
Another W-computably categorical field K
Using noncomputable fields
New question: how many structures....?
Using computable fields
Using all subfields of
Isomorphism types of subfields of 0
Answers about Rx and HTP(K)
Summarizing the theorem
Answer to another question
Taught by
Joint Mathematics Meetings
