Course syllabus

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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. 

Registration

You will be able to register on the course one week before it starts, so around August 26th. When you have registered for the course you will get access to more course information and can start work with the modules.

You can find information regarding registration here.

Teachers

Fredrik Engström Tjeerd Fokkens

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

There is an English - Swedish dictionary of mathematical terms that can be useful for some of you. 

Examination

The course is assessed through individually hand-ins, one for each module, and an individual oral exam over Zoom.

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. We hope to be able to give you feedback on your hand-ins within a week of submission. If you fail you will get a new chance to submit new solutions. The formal deadline for all hand-ins is December 20th so that we have a chance to schedule an oral exam in January before the end of the course. 

To pass the course you need to pass all hand-ins and also the oral exam. More information about the oral exam will be made available later. 

Please note that the quizzes are not obligatory, but highly recommended.

Course plan

There will be an introductory meeting over Zoom on 4 September 17:00 - 18:00. This meeting is not obligatory, but recommended to attend. Zoom-link: https://gu-se.zoom.us/j/64782810834?pwd=UNCgSXKRHwVZtveEt0kMjSVMEJ1Pwc.1 

Before the meeting, please go through the modules Introduction and Preliminaries. 

Please see the Modules page (see menu) for the course plan.

There will be possibilities to meet the teachers and ask questions over zoom. 

Zoom meetings

We will have five zoom meetings, one per module/hand-in assignment, following the recommended schedule you'll find on the Welcome page. These are Q&A sessions and we will prioritize questions on the specific module, but if time permits you're welcome to ask questions on other parts of the course as well. 

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 Anja Ehn, Anja.ehn@gu.se answers questions about registration, examination administration, study interruptions, study breaks, certificates, etc. 
  • Education coordinator Peter Johnsen, peter.johnsen@gu.se.

Student information

Learn Canvas

Checklist for new students

Student Portal

Welcome to the Department of Philosophy, Linguistics and Theory of Science

Rights and responsibilities

Cheating and plagiarism

Course summary:

Course Summary
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