The course introduces the students to the basics of axiomatic set theory and to notions such as infinite sets, cardinality or the ordinal numbers.
Requirements on student
Oral examination only. The student is assigned one topic from the list in the course overview.
Content
1. The axioms of the Zermelo-Fraenkel set theory.
2. Relations, mappings, orders.
3. Natural numbers, a construction of the real numbers.
4. Finite sets.
5. Well-orderings.
6. Ordinals.
7. Cardinality of sets.
8. Cardinals.
9. The axiom of choice.
Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully:
In view of the axiomatic treatment of set theory, the completion of An Introduction to Mathematical Logic (KMA/ML) may be an advantage for those taking up this course.
Learning outcomes
Knowledge - knowledge resulting from the course:
Upon completion of this course, students will acquire basic orientation in the subject and become capable of independent study of the literature.
Assessment methods
Knowledge - knowledge achieved by taking this course are verified by the following means:
Oral exam
Teaching methods
Knowledge - the following training methods are used to achieve the required knowledge: