Course content

Introduction to Zermelo-Fraenkel Set Theory and Gödel’s universe L of constructible sets.

Learning outcome

The student will be aquainted with the Zermelo-Fraenkel axiom system ZFC for set theory with the axiom of choice and with how ZFC may serve as a formalization of mathematics. In the first part, emphasis will be put on the well ordering concept, on ordinal numbers and transfinite recursion and induction and on the equivalence of the well ordering principle, the axiom of choice and Zorn’s lemma. In the second part, an inner model for set theory, Gödel’s L, is studied, and L is used to verify certain consistency results for set theory, including the consistency of Cantor’s continuum hypothesis.

Admission to the course

PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.

Some knowledge of first order logic will be an advantage, but it will be possible to follow the course for all master and Ph.D. students in mathematics.

Overlapping courses

Teaching

3 hours of lectures per week in common with the course MAT4640 – Axiomatic Set Theory (discontinued). In addition, students following the course will be given some extra hours of common academic supervision during the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.

Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.

Examination

1 mandatory assignment.

Final oral examination.

In addition, each PhD candidate is expected to give an oral presentation on a topic of relevance chosen in cooperation with the lecturer. The lecture has to be approved by the lecturer for the student to be admitted to the final exam.

Examination support material

No examination support material is allowed.

Grading scale

Grades are awarded on a pass/fail scale. Read more about the grading system.

Resit an examination

This course offers both postponed and resit of examination. Read more:

More about examinations at UiO

You will find further guides and resources at the web page on examinations at UiO.

Last updated from FS (Felles studentsystem) Nov. 5, 2026 8:07:11 AM

Facts about this course

Level
PhD
Credits
10
Teaching

Spring 2020

Taught according to demand and resources. Contact studieinfo@math.uio.no if you are interested in this course.

Spring semester 2020: This course will only be given as a self-study course for PhD-students who has this in their study plan.

The course is last held autumn 2022

Examination
Spring .

Examination is last held autumn 2022

Teaching language
English

Contact

Department of Mathematics