# NMAK18009U Changed: Topics in Mathematical Logic

Volume 2020/2021
Education

MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject

Content

We will cover various topics in logic and set theory, with the precise content varying from year to year, depending on the decision of the lecturer and the interests of the participants. Topics that may be covered include:

• Advanced topics in axiomatic set theory such as Gödel's constructible universe L, and independence proofs by forcing.
• Infinitary combinatorics, Ramsey theory.
• Descriptive set theory, including analysis of Borel sets, analytic sets, and if time allows, descriptive set theory in L.
• Topics in model theory, e.g. Scott sentences, types, continuous logic.
• Recursion (computability) theory, e.g. priority arguments.
Learning Outcome
• Knowledge: To display knowledge of the course topics and content.
• Skills: To be able to use the acquired knowledge to read and understand current research papers.
• Competences: The student should be able to apply the theory to solve problems of moderate difficulty within the topics of the course.

Examples of literature:

Lecture notes will be provided for some topics.

For other topics, we might use parts of the following examples of course literature:

A. Kechris: Classical Descriptive Set Theory (Springer. Note that this book is available as a pdf for free from the Springer website.)

K. Kunen: Set Theory (North Holland)

D. Marker: Model Theory (Springer)

S. Soare: Recursively enumerable sets and degrees.

The course Introductory Mathematical Logic, or a similar logic course which covers introductory elements of 1st order logic, model theory, and axiomatic set theory. Some basic knowledge of general topology and measure theory may be required for some topics, particular topics in descriptive set theory.

Academic qualifications equivalent to a BSc degree is recommended.
4 hours of lectures/week + 2 hours of exercises per week for the first 5 weeks. Then 3 weeks of project work.
• Category
• Hours
• Lectures
• 20
• Preparation
• 100
• Theory exercises
• 12
• Project work
• 54
• Exam
• 20
• Total
• 206
Continuous feedback during the course of the semester
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Continuing evaluation based on 1 problem set, and 1 written project.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Re-exam

30 min oral examination, no preparation time.

##### Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.