# Peter Koepke: Namba-like singularizations of successor cardinals

Monday, May 13, 2013, 16.30
Seminar room 1.008, Mathematical Institute, University of Bonn

Speaker: Peter Koepke (Bonn University)

Title: Namba-like singularizations of successor cardinals

Abstract:

Bukowski-Namba forcing preserves aleph_1 and changes the cofinality of aleph_2 to omega. We lift this to cardinals kappa > aleph_1: Assuming a measurable cardinal lambda we construct models over which there is a further “Namba-like” forcing which preserves all cardinals <= kappa and changes the cofinality of kappa^+ to omega. Cofinalities different from omega can also be achieved by starting from measurable cardinals of sufficiently strong Mitchell order. Using core model theory one can show that the respective measurable cardinals are also necessary. This is joint work with Dominik Adolf (Münster).