CANCELLED Gödel's Constructive Universe of Sets

Course content

The constructible universe (short: L) was introduced by Gödel, and is still an indespensable tool in set theory. L is a the minimal class model of ZFC, the Zermelo Fraenkel axiom system of set theory (including the axiom of choice) with many interesting properties: L is absolute, satisfies the generalised continuum hypothesis, global choice, and interesting combinatorial properties such as the square and diamong principles.

The course will include a short introduction to formal logic and languages, as well as an introduction to set theory, including ordinals and cardinals.

The L is defined. The proof of the diamond principle in L is discussed, as well as the beginnings of fine structure and the proof of the square principle in L.

If time permits, we will discuss large cardinals and their compatibility/incompatibility to L, as well as other inner models such as HOD (the hereditarily ordinal definable sets).

Education

MSc Programme in Mathematics

Learning outcome
  • Knowledge: To display knowledge of the course topics and content, at the level of a beginning researcher.
  • Skills: To be able to use the acquired knowledge to perform computations.
  • Competencies: To be able to produce independent proofs in extension of the acquired knowledge.

4 hours of lectures/week + 2 hours of exercises per week for 9 weeks.

ECTS
7,5 ECTS
Type of assessment
Continuous assessment
The grade will be based on three graded mandatory home exercise problem sets, which will be assigned as the course progresses. The three problem sets contribute equally to the final grade.
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)

  • Category
  • Hours
  • Lectures
  • 28
  • Exercises
  • 14
  • Preparation
  • 16
  • English
  • 58