Course syllabus

Welcome to Set theory, LOG121, 7,5 credits

This course is both part of the Master's Programme in Logic as well as available as a free standing course. The course runs in parallell with the first part of the course Logical Theory.

Course content

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.

TeachersPhoto of Fredrik Engström

The course will be taught by Fredrik Engström. You can contact Fredrik by email, fredrik.engstrom@gu.se, or give him a call at +46 - 31 - 786 6335.

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.

Schedule

The schedule for the course is available on TimeEdit. All lectures will be given at campus and streamed over zoom. The link for all the lectures and exercise sessions is the following:

https://gu-se.zoom.us/j/62482969642?pwd=NjZJZTA1a1A4ZC9lSlkyZE5hMkRkQT09 

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. 

Weekly lecture plans

Weekly lecture plans with short comments and reading instructions will be made available through the Modules page.

Examination

(updated 2020-08-25)

Please be aware that due to the special covid-19 situation the form of the examination has been altered and we will make sure that you can take the two examinations online from your home. 

There will be one sit down written examination. You will be able to take the exam from your home using Zoom. This is an individual exam and you are not allowed to collaborate or communicate with anyone during the exam. However, you are allowed to read the book, your notes and use the internet (but not to communicate or ask questions). You will need to be able to identify yourself by showing a valid id-card or passport over zoom which means that you need a computer with a camera. More information about the exams will be available later.

The hand-in problems and assignments are not obligatory to pass the course, but we strongly recommend students to take the opportunity to get feedback on your solutions. 

You can find some old exams here, but please observe that the coming exams might be slightly different in form due to the special situation:

 

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. 

Course evaluations

The course will be evaluated through a course questionnaire. A short summary of the course evaluation from last year is available here.

The course report is available here.

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. 
  • Program Coordinator Fredrik Engström, fredrik.engstrom@gu.se is responsible for programme issues and study guidance for students of the programme.
  • Student counselor Peter Johnsen, peter.johnsen@gu.se, is responsible for study guidance of the free-standing course.

Plagiarism and academic integrity

(updated 2020-08-25)

Please take the time to go through the module Academic Integrity 1 to make sure that you understand what plagiarism is, why one should not plagiarise, and what happens if one does plagiarise.

Student information

Learn Canvas

Checklist for new students

Student Portal

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

Study Environment and Rules

Fire protection information

Course summary:

Date Details Due