NMAK18009U Topics in Mathematical Logic
MSc Programme in Mathematics
MSc Programme in Mathematics w. a minor subject
Topics that may be covered are: Axiomatic set theory, ordinals, cardinals. Basic structure of the set theoretic universe V. Gödel's constructible universe L and equiconsistency. Infinitary combinatorics. Descriptive set theory, including analysis of Borel sets, analytic sets, and if time allows, descriptive set theory in L. Model theory. Recursion (computability) theory.
Knowledge: The student should, by the end of the
course, know the axioms of set theory, ordinals, cardinals,
and the struture of the set theoretic universe V. The student
should know the construction of the model L, as well as important
combinatorial principles that are true in L, such as the Continuum
Hypothesis. The student should know what Borel and analytic sets
are, and what properties these sets have, and should know how to
prove basic theorems about these types of sets.
Skills: The student should be able to apply set theoretic concepts and result mentioned in the previous paragraph to account for the structure of the universe V, the structure of the constructible universe L, the special combinatorial principles that hold in L, and to account for the structure of Borel and analytic sets.
Competences: The student should be able to formulate the main results of the course, check whether they are applicable in a concrete problem and use them to solve it.
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.
- Project work
- Theory exercises
- 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.