The main purpose of this course is to overview novel set-theoretic and combinatorial techniques. We will especially focus on constructing interesting uncountable structures with prescribed combinatorial behaviour. These structures will be used to investigate and solve problems from topology, finite and infinite combinatorics and graph theory.
Requirements for the seminar are covered in a regular Logic 1 lecture. We assume knowledge of structures, elementary substructures, transfinite induction and recursion, as well as basic knowledge of topology.
We meet for a Vorbesprechung, where the seminar’s topic is introduced again and in more detail on Monday, July 10, 16:00, at SR1D on the first floor of the main building.
Gödel formulated the axiom of constructibility and thereby showed that the continuum hypothesis is consistent with the standard axiom system of set theory, ZFC. This area of set theory may be explored with not many prerequisites at hand. The topics of the seminar will be: Introduction of L, the constructible universe; proof of ZFC and the generalized continuum hypothesis in L; combinatorial principles and large cardinals in L; Jensen's covering lemma for L. Details will be discussed and a handout with topics for talks will be provided at the preliminary meeting, see below.
- Lehrende/r: Ralf-Dieter Schindler