Graduate seminar on 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.
You can still participate, for instance one of the talks 7.-9. is still available.
Programm
- 1. The constructible universe, ZFC in L, absoluteness of constructibility - Jech chapter 13 - Jens Krewald
- 2. Global well-order of L, condensation, GCH, acceptability (as us for details) - Jech chapter 13 - Niels Ranosch
- 3. diamond_kappa(S), large cardinals in L - Schindler Theorem 5.35, Kanamori Exercise 3.1 - Thijs Jacobs
- 4. Nonexistence of elementary j:V->V (exercise), statement of the covering theorem, consequences of covering: weak covering, SCH - various sources, ask us for details - Nikolina Barisic
- 5. Hyperfine structure - Koepke 53-57 - Milos Tepavcevic
- 6. The fine hierarchy - Koepke 82-86 - Joshua Chen
- 7.-9. Proof of covering - Koepke 107-118 - Andreas Lietz, Sebastian Gurke, tba
Literatur
- [1] Jech: Set Theory
- [2] Kanamori: The higher infinite
- [3] Koepke: Simplified constructibility theory - unpublished lecture notes
- [4] Schindler: Set Theory