MAT9640 - Axiomatic Set Theory
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Course content
Introduction to Zermelo-Fraenkel Set Theory and Gödel’s universe L of constructible sets.
Learning outcomes
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 participate in this course you must have an admission to a Ph.D.-programme at a Norwegian University or University College.
If you do not have an admission to the Ph.D.-Programme in Science at The Faculty of Mathematics and Natural Sciences at UiO, you have to apply for hospitantstatus (norwegian text) . For more information, please contact the Department.
The examination in this course is not available for external candidates. Only students admitted to the course may sit for the examination.
Prerequisites
Recommended prior 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.
Overlap
10 credits against MAT4610 - Axiomatic set theory. 10 credits against MAT9610 - Axiomatic set theory. 10 credits against MAT4640 - Axiomatic Set Theory. 10 credits against MA360.
For information about the potential partial overlap with other courses, contact the Department.
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.
Exam information
One mandatory assignment needs to be passed. Final oral exam(counts 100% of the grade).
Each PhD-student will give a 45 minutes lecture on a given topic related to, but not within, the curiculum. The lecture is to be aimed at the other students and must be accepted by the teacher.
Rules for compulsory assignments at the Department of Mathematics.
Exam resources
No special exam resources are allowed.
Language of examination
Students may, on subjects taught in Norwegian and the examination form is written exam, ask for the exam paper in Bokmål, Nynorsk or English. Closing date for registering the chosen examination language is September 1st for the fall semester and February 1st for the spring semester.
Please view the web page of the Faculty of Mathematics and Natural Sciences on how to proceed
Subjects taught in English will offer the exam paper in English only.
This rule also applies for subjects where the exam form is dependent on the number of students and written exam is chosen by the teaching staff.
Assessment and grading
Students are awarded either a passing or a failing grade. Read more about the grading system .
Explanations and appeals
A student may appeal against an awarded grade and/or file a formal complaint about exam procedures
Possibility of make-up exams and re-takes
Students who due to illness or other valid reason of absence were unable to sit for their final exams may apply for participation in deferred examinations. Deferred examinations are arranged either later in the same semester or early in the semester following the exam in question. Documentation of valid reasons for absence from the regular exam must be submitted upon application to participate in deferred examinations.
Students who have failed an exam, who withdraw during an exam, and students who wish to retake an exam to achieve a better grade may not participate in deferred exams, but may retake the exam when it is regularly scheduled.
Information about deferred and new examination (also called repeat examination) is found here
Withdrawing from exams and limits on re-takes
A student can sit for this exam up to 3 times. If a student wishes to withdraw from the exam, s/he must do this in StudentWeb at least two weeks prior to the first day of the exam. Failure to do so will be counted as one of the three opportunities to sit for the exam.
Exam options for students with special needs
Students may apply for access to alternative exam resources or exam forms on the basis of chronic illness and/or special needs that create a marked disadvantage to other students in the exam situation. Mothers who are breastfeeding may apply for extra time to complete the exam.
Evaluation of this course
Feedback from our students is essential to us in our efforts to ensure and further improve the high quality of our programmes and courses. As a student at the University of Oslo you will therefore be asked to participate in various types of evaluation of our courses, facilities and services. All courses are subject to continuous evaluation. At regular intervals we also ask students on a particular course to participate in a more comprehensive, in-depth evaluation of this course, a so called "periodic evaluation".
Contact us
Department of Mathematics
Visiting address:
Niels Henrik Abel's building, Moltke Moes vei
Visiting hours:
Monday-friday 09:00-14:30
Postal address:
P.O.box 1053, Blindern
NO-0316 Oslo
Fax: +47 22 85 43 49
E-mail: studieinfo@math.uio.no
Web: http://www.mn.uio.no/math/english/