2nd Semester 2010/11: Interpretability and Incompleteness
- Dick de Jongh and Albert Visser
If you are interested in this project, please contact Dick by email.
This project is given on the request of four students. One or two other students can join if they have a proven interest in the subject, and some background in metamathematics. The students will work as a group, dividing tasks, and will be evaluated as a group.
- At this moment three different topics are under consideration, from which one will be chosen.
- Study of Friedman's lecture on the degrees of interpretability of finitely axiomatized theories. Read and study: http://www.math.osu.edu/~friedman/manuscripts.html, no. 60 of Preprints, Drafts and Abstracts, lecture 1.
- Study of the lattice of chapters (very general theories of arbitrary complexity and cardinality). Read, study, and relate to (1): Mycielski, J. and Pudlák, P. and Stern, A.S., A lattice of chapters of mathematics (interpretations between theorems), Memoirs of the American Mathematical Society, no. 426, 1990.
- Development of classical metamathematics (the incompleteness theorems etc.) in the context of a very weak set theory (in development by Albert Visser).