Course syllabus

LOG120: Set theory, 7.5 credits

The course treats Zermelo-Fraenkel set theory, ZFC, formulated in first-order logic, beginning with a set theoretical construction of the natural and real number systems. Ordinal and cardinal numbers are presented and strong emphasis is placed on the cumulative hierarchy and on the role of the axiom of choice in the axiomatization of the concept of set.

Literature

The course is based on Classic Set Theory by Derek Goldrei.

Schedule

Please see the TimeEdit schedule.

The course starts September 11 and the exam is planned for October 30. 

Course plan

Please see the Modules page for the course plan.

Learning outcomes

On successful completion of the course the student will be able to:

Knowledge and understanding

• describe and demonstrate an understanding of the central concepts, methods, and constructions in set theory.
• describe the various types of set theoretical objects that can be constructed using the different axioms, with a special focus on the axiom of choice.
• demonstrate an understanding of set theory as a sub-area of logic and contrast it with other areas of logic.
• at a general level account for the historical development of axiomatic set theory.

Competence and skills

• formulate and present set theoretical constructions of number systems including the natural and real numbers, as well as verify their most central properties using the axioms of set theory.
• formulate, derive and apply basic arithmetic for cardinal and ordinal numbers.
• formulate and present proofs of the most important results in the course as well as of lemmas that are used in the proofs.

Judgement and approach

• critically discuss, analyse and evaluate the results in the course as well as their applications.
• show awareness of the relationship between set theory and mathematics.

See the course syllabus for more information.