Schedule, syllabus and examination date

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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.


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.


Recommended previous knowledge

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

For information about the potential partial overlap with other courses, contact the Department.


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

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.


mandatory assignment.

Final oral examination. 

In addition, each PhD student is expected to give a 45-minute lecture 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.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

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

Explanations and appeals

Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.


The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course






Spring 2015

Spring 2014

Spring 2012

Spring 2011

Taught according to demand and resources. If you want to attend the course, please send an e-mail to


Spring 2015

Spring 2014

Spring 2012

Spring 2011

According to demand and resources.

Teaching language


The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.