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Topics in Mathematical Logic
Provider: Faculty of Science

Activity no.: 5572-18-07-31 
Enrollment deadline: 19/11/2018
Tilmelding : Topics in Mathematical Logic
ECTS credits7.50
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time19.11.2018, at: 08:00 -
27.01.2019, at: 00:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserAsger Dag Törnquist    E-mail address: asgert@math.ku.dk
Teaching languageEnglish partially in English
Semester/BlockBlock 2
Scheme groupC
Exam formContinuous assessment
Exam formContinuous assessment
Exam detailsContinuing evaluation based on three problem sets graded on the 7-point scale. Each problem set caries equal weight towards the final grade. All aids allowed. 7-point grading scale. No external censorship.
Exam aidsAll aids allowed
Course workload
Course workload categoryHours
Lectures20.00
Exercises10.00
Preparation110.00
Project work66.00
Sum206.00
Learning outcome
Knowledge: The student should, by the end of the course, know the axioms of set theory, ordinals, cardinals, and the struture of the set theoretic universe V. The student should know the construction of the model L, as well as important combinatorial principles that are true in L, such as the Continuum Hypothesis. The student should know what Borel and analytic sets are, and what properties these sets have, and should know how to prove basic theorems about these types of sets.

Skills: The student should be able to apply set theoretic concepts and result mentioned in the previous paragraph to account for the structure of the universe V, the structure of the constructible universe L, the special combinatorial principles that hold in L, and to account for the structure of Borel and analytic sets.

Competences: The student should be able to formulate the main results of the course, check whether they are applicable in a concrete problem and use them to solve it.

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)

Target group
Knowledge: The student should, by the end of the course, know the axioms of set theory, ordinals, cardinals, and the struture of the set theoretic universe V. The student should know the construction of the model L, as well as important combinatorial principles that are true in L, such as the Continuum Hypothesis. The student should know what Borel and analytic sets are, and what properties these sets have, and should know how to prove basic theorems about these types of sets.

Skills: The student should be able to apply set theoretic concepts and result mentioned in the previous paragraph to account for the structure of the universe V, the structure of the constructible universe L, the special combinatorial principles that hold in L, and to account for the structure of Borel and analytic sets.

Competences: The student should be able to formulate the main results of the course, check whether they are applicable in a concrete problem and use them to solve it.

Teaching and learning methods
CHANGED FOR THE STUDY YEAR 2018/19
4 hours of lectures/week + 2 hours of exercises per week for 8 weeks.

Content
Axiomatic set theory, ordinals, cardinals. Basic structure of the set theoretic universe V. Gödel's constructible universe L and equiconsistency. Infinitary combinatorics. Descriptive set theory, including analysis of Borel sets, analytic sets, and if time allows, descriptive set theory in L.

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