Student seminar Categorical Logic

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: Ludo van Wieringen, Quinn van der Velden, Rob Schellingerhout. Visitors: Alkis Ioannidis, Sara Rousta.

The meetings are on Monday afternoons 15-17, in room Duistermaat. First meeting: 12 february 2024.

Requirements, Learning Goals and Grading

In view of the reduced number of participants, we have opted for a hybrid form: seminar/reading group. Every meeting, a specified slice of material (sections from research papers, parts of research monographs, preprints etcetera) is selected; one of the participants is responsible for spotting difficulties in the text, gaps in proofs and so on, and for fixing these. This participant (the "speaker") may also be called to present stuff at the blackboard.

Every speaker 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.

Attendance is mandatory.

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

We work through a number of (pre)publications: preprints, research papers, chapters of books and the like:

  1. van Oosten: Basic Category Theory and Topos Theory.
  2. Carsten Butz: Regular Categories and Regular Logic.
  3. Andrew M. Pitts: Categorical Logic.
  4. Ieke Moerdijk: Sheaves and Logic.
  5. Andrew M. Pitts: Conceptual Completeness for first-order intuitionistic logic

Planning

12/2/24: Ludo: sections 1,2 of Butz. Homework: Exercise 93 of Van Oosten, p.45.
Caveat: instead of the commutativity required in that exercise, prove commutativity up to isomorphism.
19/2/24: Quinn: sections 4,5 of Butz. Homework. Solution.
26/2/24: Rob: section 6 of Butz and 4.1,4.2 of Pitts (Categorical Logic). Homework. Solution.
4/3/24: Jaap: 4.3,4.4, 5.1--5.2 of Pitts (Categorical Logic). Homework. Solution.
11/3/24: Ludo: 5.3--5.4 of Pitts. Homework. Solution.
18/3/24: Quinn: remainder of section 5 of Pitts. Homework. Solution.
25/3/24: Rob: first sections of Moerdijk's, up to and including Forcing. Homework. Solution.
1/4/24: no seminar (Easter Monday).
8/4/24: Jaap
15/424: Ludo. Freyd's disproof of the Axiom of Choice. Homework.
22/4/24: Ludo (continued)
29/4/24: Quinn. Homework. Solution.
13/5/24: Rob. Homework. Solution.
20/5/24: no seminar (Whit Monday)
27/5/24: Evaluation of seminar

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