Graduate Seminar on Set Theory (S4A4): Stationary tower forcing
Organizers
- Prof.Dr. Peter Koepke
- Dr. Philipp Schlicht
- Dr. David Schrittesser
Time and location
Wednesdays 10-12 in room N0.003
Prerequisites: forcing as in Models of set theory I
Contents
A generic ultrafilter on a regular cardinal kappa may be added by forcing with the stationary subsets ordered by inclusion. This is of particular interest when the ultrapower of V with the generic ultrafilter is well founded. When forcing with the stationary tower, a family of embeddings is amalgamated into a generic almost huge embedding, starting from a Woodin cardinal in the ground model. In this seminar, we will develop stationary tower forcing following Paul Larson's book 'The stationary tower', and look at applications such as forcing absoluteness of the theory of the Chang model from a proper class of Woodin cardinals.
Plan
- 12 October Philipp Schlicht Measurable cardinals and generic ultrapowers
- 19 October David Schrittesser Generalized stationary sets
- 26 October David Schrittesser The stationary tower
- 02 November Peter Koepke Forcing properties of the stationary tower
- 09 November Peter Koepke Forcing properties of the stationary tower continued
- 10 November (in room N0.008) Ronja Reese Completely Jonsson cardinals
- 21 January 10.00-12.00 Mona Rahn Properties of the generic embedding
- 21 January 13.30-15.30 Anne Fernengel Wellfoundedness of the ultrapower part 1
- 22 January 10.00-12.00 Marios Koulakis Wellfoundedness of the ultrapower part 2
- 22 January 13.30-15.30 Miguel Moreno Absoluteness of the theory of the Chang model