Topics in Mathematical Logic
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.
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
- 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.
4 hours of lectures/week + 2 hours of exercises per week for the first 5 weeks. Then 3 weeks of project work.
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 student must have completed the course Introductory
Mathematical Logic, or an equivalent 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.
- 7,5 ECTS
- Type of assessment
- Type of assessment details
- Continuing evaluation based on 1 problem set, and 1 written project.
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
Criteria for exam assessment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Single subject courses (day)
- Theory exercises
- Project work
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 2
- No limit
The number of seats may be reduced in the late registration period
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Asger Dag Törnquist (6-687a6e6c797b4774687b6f35727c356b72)
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Courseinformation of students