MAT4640 – 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
Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.
Prerequisites
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 MAT9640 – Axiomatic Set Theory
*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department
Teaching
3 hours per week throughout 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.
Examination
Final oral examination.
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 scale from A to F, where A is the best grade and F is a fail. 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.
Evaluation
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.