Welcome to Set theory, 2022, LOG121, 7,5 credits

This course is both part of the Master 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.

Teachers  

The course will be taught by Fredrik Engström and Tjeerd Fokkens. 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.

Introduction

See Schedule below for time and location of the first lecture.

Schedule

A preliminary schedule for the course is available through TimeEdit. All lectures will be given at campus.

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

There will be one sit down written examination. This is an individual closed book exam and you are not allowed to bring any text, book, computer or other device to the exam. Please read the general information about exams.

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 written solutions. 

Example of exam questions can be found here: exam_2020_oct_LOG121.pdf and here: exam_2019_oct_LOG120.pdf  (note that the exam from 2020 was an open book exam).

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 was evaluated through a course questionnaire. A summarizing report is available: Course_report_with_evaluation_LOG121_2022.pdf 

A short summary of the course evaluation from last year is available: Course_report_with_evaluation_LOG121_2021.pdf 

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 Peter Olsson, peter.olsson.2@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

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