MAT9640 – Axiomatic Set Theory
Course description
Course content
Introduction to Zermelo-Fraenkel Set Theory and G?del’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, G?del’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.
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
- 10 credits overlap with MAT4610 – Axiomatic set theory (discontinued).
- 10 credits overlap with MAT9610 – Axiomatic set theory (discontinued).
- 10 credits overlap with MAT4640 – Axiomatic Set Theory.
- 10 credits overlap with MA360.
- 10 credits overlap with MA360.
Teaching
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.
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
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
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.