2nd Semester 2018/19: Research topics in set theory
In this project, students choose their own "research topic" in set theory or a closely related field, such as Foundations of Mathematics, conduct an independent study and present their results. The focus on "research topic" does not mean that students should conduct their own research, but rather that their study should focus on research papers and material that goes beyond standard textbooks. "Set Theory" is understood broadly to include topics such as: alternative foundations of mathematics, set theory based on other logics and philosophical approaches.
Students who already have a clear preference can suggest their own papers for study; others can suggest an approximate area of interest and we can decide on the exact project together.
Some suggested topics:
- Infinitary models of computation
- Generalized Baire Spaces / Generalized Descriptive Set Theory
- Modal logic of forcing
- Set Theory of Strong Logics
- Class theories
- Intuitionistic/Constructive Set Theory
- Other non-classical Set Theory
The students conduct independent research facilitated by individual meetings, followed by a talk of 2h. Afterwards, the students write a short summary of their research in their own words.
Knowledge of basic set theory and logic. Students with advanced knowledge of set theory will have access to a wider variety of research topics, but those with basic knowledge should be able to find a suitable topic as well.
PASS/FAIL, based on the public presentation and the written summary.