Graduate seminar on Set Theory (S4A4)
Dozenten
- Prof. Dr. Peter Koepke
- Dr. Peter Holy
- Dr. Philipp Lücke
- Dr. Philipp Schlicht
Zeit und Ort
- Tuesday 16.15-18.00 N0.008
- Beginn: 10.10.2017
Contents
There is a least proper class transitive model of set theory - the constructible universe L - which was constructed by Gödel. We study its properties and aim for a proof of Jensen's covering theorem via a variant of fine structure theory. The covering theorem states that either there is a nontrivial elementary embedding from L to L, or the universe is close to L in a precise sense.
Programm
- 1. The constructible universe L, ZFC in L and absoluteness of constructibility - Jech chapter 13 - Jens Krewald
- 2. A global wellorder of the constructible universe, condensation, GCH and acceptability - Jech chapter 13 - Chiara Maziotta
- 3. The diamond principle and Suslin tres - Jech, Schindler - Thijs Jacobs
- 4. Non-trivial elementary embeddings, zero sharp and consequences of the covering theorem - Niels Ranosch
- 5. An introduction to hyperfine structure - Koepke pp. 53-57 - Nikolina Barisic
- 6. The fine hierarchy - Koepke 82-86 - Joshua Chen
- 7.-9. A proof of the covering theorem - Koepke pp. 107-118 - Andreas Lietz, Sebastian Gurke
Literatur
- [1] Jech: Set Theory
- [2] Kanamori: The higher infinite
- [3] Koepke: Simplified constructibility theory - unpublished lecture notes
- [4] Schindler: Set Theory