## 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*