Bonn Mathematical Logic Group

Graduate Seminar on Set Theory (S4A4): Stationary tower forcing

Organizers

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
The remaining talks will take place on January 21th and 22th (in room N0.003 as usual).
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

 

Last changed: 05 December 2011