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Capita Selecta: Set Theory, Model Theory
2008/2009; 1st Semester
Institute for Logic, Language & Computation
Universiteit van Amsterdam

Instructors: Dr Benedikt Löwe
Drs Yurii Khomskii
Drs Brian Semmes
Vakcode: MoLCSMT6
Time: Monday, 9-11
Place: See table below
ECTS credit points: 6
Course language: English
Intended Audience: M.Sc. students of Logic and Mathematics

This course is offered as a reading course with supporting lectures and exercises. The students are required to read a certain number of pages from Kunen's book (see below) before the lecture. During the lecture, we shall present the most important results from the assigned pages and answer questions. In addition to the lectures, there will be homework that is graded.

Contents and literature:

The course will cover relative consistency proofs in set theory, focusing on the important techniques of submodels, inner models, ordinal definability and constructibility.

We shall read Chapters IV, V and VI of Kunen's book, Set Theory. An Introduction to Independence Proofs. (with a little bit of extra reading for background material on combinatorial principles).

Assessment and Grading:

There will be regular homework assigments announced below on this webpage. The course grade will be assigned based on an oral exam. In order to be admitted to the oral exam, you need to properly solve 50% of the homework problems.

We shall arrange two dates for the oral exams in order to accommodate those who would like to do the exam in December and those who would like to have some extra study period. The first exam date will be Thursday 18 December 2008, the second will be at the end of January 2009. Details will be announced in due time. The oral exam will be a 30-minute exam in the presence of all three teachers testing your understanding of the material covered in class.

Date and Time Location Material to read before class. Homework assigned (with due date)
22 September, 10-11 P-0.15A Introductory meeting. No required reading. None.
29 September, 9-11 P-0.15A p.110-124 None.
6 October, 9-11 P-0.15A p.124-133 Chapter IV. (1), (4), (5), (7), (8), (14). Errata
Due: 20 October.
13 October, 9-11 P-0.15A p.133-137 None.
20 October, 9-11 P-0.15A p.137-141 Chapter IV. (18), (19), (23), (29), (30).
Due: 3 November.
27 October, 9-11 P-0.15A p.152-157 None.
3 November, 9-11 P-0.15A p.158-163 Chapter V. (1), (4), (5), (6), (7), (9).
Due: 17 November.
10 November, 13-15 C-2.12 p.165-169 None.
17 November, 13-15 P-3.27 p.169-173 Chapter VI. (2), (3), (4).
Due: 24 November
24 November, 13-15 J/K-B.58 p.172-177 Chapter VI. (6), (7).
Due: 1 December
1 December, 13-15 J/K-B.58 p.68-70 Chapter II. (35), (36).
Due: 8 December
8 December, 13-15 J/K-B.58 p.80-86, but excl. 7.10, 7.11 and 7.12
Also, read 76-80 for background/revision
Chapter II. (51), (52).
Due: 15 December
15 December, 13-15 J/K-B.58 p.177-179 None.

Last update : 2 December 2008