Entry requirements

60 credits in mathematics.

Learning outcomes

In order to pass the course (grade 3) the student should be able to

• use set theoretic axioms to prove the existence of certain sets;
• use the concepts of class and set in a correct way, and know the difference between them;
• use induction on well ordered sets;
• construct functions recursively;
• use operations on ordinals and cardinals;
• compare and compute the cardinalities of sets;
• formulate the Axiom of Choice, Zorn's Lemma and the Well-ordering Theorem;

Content

Basic set theoretic concepts and set theoretic formulas.

Relations and functions seen as sets.

Partial orders and equivalence relations.

Zermelo-Fraenkel axioms for set theory

The concepts of class and set.

The concepts of inductive sets and set theoretic construction of the natural numbers.

The sizes of sets via the notion of cardinality.

Well-orderings. Transfinite recursion.

The Axiom of Choice, Zorn's Lemma and the Well-ordering Theorem.

Filters and ideals.

Ordinals and cardinals, operations on these and rules for said operations.

Instruction

Lectures

Assessment

Written examination at the end of the course combined with assignments given during the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.