NMAK18009U Changed: Topics in Mathematical Logic
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
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.
- 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.
Academic qualifications equivalent to a BSc degree is recommended.
- Theory exercises
- Project work
- 7,5 ECTS
- Type of assessment
- Continuous assessmentContinuing 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
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.