Bonn Mathematical Logic Group

Graduate seminar on on Set Theory (S4A4)


Dozenten

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[3] Koepke: Simplified constructibility theory - unpublished lecture notes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

Letzte Änderung: 24 July 2017