Teacher is Jaap van Oosten. He can be found at room 5.07, tel. 3305. Email: j.vanoosten AT uu.nl
Participants: Feike van Ammers, Tim Baanen, Jack Davies, Bart Keller, Ieke Moerdijk, Loe van Montfort, Matteo Spadetto, Jetze Zoethout.
The meetings are on Wednesdays 13:15--15:00, in room 610, HFG. First meeting: Week 7 (Wednesday February 13, 2019).
Every student presents material, in a blackboard talk. It is permitted to distribute handouts to the audience. Every presentation lasts twice 45 minutes minus 5 minutes (for discussion). Students of adjacent presentations are encouraged to work together.
Additionally, every student formulates a homework exercise, which the other participants solve, 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 presents twice.
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%).
A celebrated theorem of Makkai, called "Conceptual Completeness for First-Order Logic" states that a first-order theory can be (up to suitable equivalence) recovered from the pretopos-completion of its category of models.
Recently, a strengthening of this result has been given by Jacob Lurie, and laid down in the text "Ultracategories", which can be downloaded here. We intend to work through this text.
Terug naar de basis.