Course syllabus
Introduction to Set theory
The course treats Zermelo-Fraenkel's set theory, ZFC, formulated in first-order logic and takes its starting point in the set theoretical construction of the natural numbers and how set theory can constitute a foundation for mathematics. Furthermore, properties of infinite sets are treated, with a focus on cardinality and properties of well-orderings. The cumulative hierarchy is discussed as well as the role of the axiom of choice in the axiomatisation of the concept of set.
This is a distance course.
Teachers
Registration
You will be able to register on the course one week before it starts. When you have registered for the course you will get access to more course information.
You can find information regarding registration here.
Literature
The course uses the book Classic Set Theory by Derek Goldrei. Any edition of the book should be fine. Please observe that the book is electronically available through the university library.
The course covers roughly the following sections of the book, for more precise reading instructions, please see the individual modules.
- Chapter 1: Full chapter
- Chapter 3: Full chapter (some parts can be skipped)
- Chapter 4: Full chapter
- Chapter 5: 5.1 - 5.2, and 5.4
- Chapter 6: Full chapter
- Chapter 7: Full chapter
- Chapter 8: 8.1 - 8.4
Examination
The course is assessed through individually hand-ins, one for each module, and a written exam.
Once you have completed a module you should solve the hand-in exercises on your own (collaboration or getting help is not allowed) and submit your solutions in Canvas. These will be marked and returned to you by one of the teachers with a pass or non-pass grade. You may resubmit until you pass.
To pass the course you will also need to do the written exam that is planned for the 21 December. This exam can be taken in your home and more information is available here: Assignments.
Please note that the quizzes are not obligatory, but highly recommended.
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 axioms,
- 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 the natural numbers as well as verify their most central properties by means of the axioms of set theory,
- formulate and derive basic properties concerning cardinality and well-orderings,
- formulate and present proof of the most important results in the course,
Judgement and approach
- show awareness of the relationship between set theory and mathematics.
See the course syllabus for more information.
Special pedagogical support
If you have a disability and are in need of special pedagogical support please see the information available at the student portal.
Contact information
- Course coordinator Fredrik Engström, fredrik.engstrom@gu.se answers questions about the course content, literature and schedule.
- Education administrator Linda Aronsson, linda.aronsson@gu.se answers questions about registration, examination administration, study interruptions, study breaks, certificates, etc.
- Student counselor Peter Johnsen, peter.johnsen@gu.se, is responsible for study guidance of the free-standing course.
Student information
Welcome to the Department of Philosophy, Linguistics and Theory of Science
Course summary:
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