Faculty of Science

Topics in Mathematical Logic
Provider: Faculty of Science

Activity no.: 5572-20-07-31
	Enrollment deadline: 16/11/2020

Place

Department of Mathematical Sciences

Date and time

16.11.2020, at: 08:00 - 29.01.2021, at: 16:00

Regular seats

ECTS credits

7.50

Contact person

Nina Weisse E-mail address: weisse@math.ku.dk

Enrolment Handling/Course Organiser

Asger Dag Törnquist E-mail address: asgert@math.ku.dk

Written language

English

Teaching language

English

Semester/Block

Block 2

Scheme group

Exam form

Course participation

Exam form

Continuous assessment

Exam details

Information will follow

Course workload

Course workload category	Hours
Lectures	20.00
Preparation	100.00
Theory exercises	12.00
Project work	54.00
Exam	20.00

Sum	206.00

Content

We will cover various topics in logic and set theory, with the precise content varying from year to year, depending on the decision of the lecturer and the interests of the participants. Topics that may be covered include:

- Advanced topics in axiomatic set theory such as Gödel's constructible universe L, and independence proofs by forcing.
- Infinitary combinatorics, Ramsey theory.
- Descriptive set theory, including analysis of Borel sets, analytic sets, and if time allows, descriptive set theory in L.
- Topics in model theory, e.g. Scott sentences, types, continuous logic.
- Recursion (computability) theory, e.g. priority arguments.

Learning outcome

Knowledge: To display knowledge of the course topics and content.

Skills: To be able to use the acquired knowledge to read and understand current research papers.

Competences: The student should be able to apply the theory to solve problems of moderate difficulty within the topics of the course.

Literature

Examples of literature:
Lecture notes will be provided for some topics. For other topics, we might use parts of the following examples of course literature:
A. Kechris: Classical Descriptive Set Theory (Springer. Note that this book is available as a pdf for free from the Springer website.)
K. Kunen: Set Theory (North Holland)
D. Marker: Model Theory (Springer)
S. Soare: Recursively enumerable sets and degrees.

Teaching and learning methods

4 hours of lectures/week + 2 hours of exercises per week for the first 5 weeks. Then 3 weeks of project work.

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