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.

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[3] Koepke: Simplified constructibility theory - unpublished lecture notes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

Letzte Änderung: 24 July 2017