Student seminar Set Theory (WISM433)

Teacher, Time and Venue, Participants

Teacher is Jaap van Oosten. He can be found at room 5.07, tel. 3305. Email: j.vanoosten AT uu.nl

Participants: Nils Donselaar, Daniel Sempaio, Saskia van den Hoeven, Martijn den Besten, Dion Hartmann, Christian Nesenberend, Hodei Rodriguez, Jan Rooduijn, Patrick González, Javier Mágan, Jetze Zoethout, Sven Bosman, Tom de Jong, Anton Golov

The meetings are on Fridays 11:00 (sharp!)--13:00, in MIN 204. First meeting: Week 37 (Friday September 11) 2015.

Requirements, Learning Goals and Grading

Every student presents material, in a blackboard talk. It is permitted to distribute handouts to the audience. Students work in pairs; each session there will be two presentations of 45 minutes (but in each presentation, leave 5 minutes for discussion).

Additionally, every pair of students formulates a homework exercise, which the other participants do, and hand in to the speaker a week later. The speaker then grades this work and hands everything (including a model solution) to the teacher. The teacher, after examination, hands the grades to the participants. Make also a grading scheme: if an exercise consists of more than one part, tell the students what each part is worth.

In the course of the seminar, every student participates in three presentations in pairs.

Attendance is compulsory.

Learning goals are:
1. Student is able to rework a given text into a coherent and understandable presentation
2. Student has good understanding of the mathematics in the field of the seminar
3. Student can formulate relevant and challenging exercises
4. Student develops collaboration and communication skills

Your final grade is composed of your grade for the presentation (40%, of which 20% for understanding the mathematics and 20% for communicating it), the formulation and grading of the homework exercise (10%) and your solutions to the other speakers' exercises (50%).

Subject Matter of the Seminar

Model Theory for Set Theory has to be nonstandard. Gödel's Incompleteness Theorems imply that we cannot define a model for ZF(C) in the usual way. Gödel himself defined an interpretation of ZF in itself: the Constructible sets. Cohen invented "forcing models".

In this seminar, we shall concentrate on "Boolean-valued models".

Reading Material

The book "Set Theory - Boolean-Valued Models and Independence Proofs" by John L. Bell, third edition (Oxford Logic Guides 47, Clarendon Press 2005).

Schedule

Week 37
Friday September 11: Introduction and Programme.
Week 38
Friday September 18: Sven and Jetze: Handout. Homework exercise 1. Model Solution 1.
Week 39
Friday September 25: Tom and Dion: Handout. Homework exercise 2. Model Solution 2.
Week 40
Friday October 2: Saskia and Jan: Handout. Homework exercise 3. Model Solution 3.1. Model Solution 3.2.
Week 41
Friday October 9: Martijn and Anton: Handout. Homework exercise 4.Model Solution 4
Week 42
Friday October 16: Christian and Nils: Homework exercise 5. Model Solution 5.
Week 43
Friday October 23: Daniel and Dion: Homework exercise 6.
Week 44
Friday October 30: No seminar (teacher is abroad)
Week 45
Friday November 6: Sven and Jetze: Handout. Homework exercise 7. Model Solution 7.
Week 46
Friday November 13: Tom and Saskia: Homework exercise 8. Model Solution 8, part 1 and 2. Model Solution 8, part 3.
Week 47
Friday November 20: Seminar will be 9:00--11:00 in room 610 of the Freudenthal Building. Martijn and Christian: Handout. Homework exercise 9. Model Solution 9.
Week 48
Friday November 27: Jan and Nils: Homework exercise 10. Model Solution 10.
Week 49
Friday December 4: Anton and Daniel: Homework exercise 11. Model Solution 11.1
Week 50
Friday December 11: Tom and Martijn: Homework exercise 12. Model Solution 12
Week 51
Friday December 18: Sven: Handout. Homework exercise 13. Model Solution 13
Week 1
Friday Januari 8, 2016: Dion, Christian and Patrick: Handout. Homework exercise 14. Model Solution 14.
Week 2
Friday January 15: Nils and Jetze: Handout Jetze. Handout Nils. Homework exercise 15-. Model Solution 15.
Week 3
Friday January 22: Anton and Jan: Homework exercise 16-Anton. Handout and Homework exercise 16-Jan.

Terug naar de basis.