# Namba-like singularizations of successor cardinals

## Peter Koepke

### Rheinische Friedrich-Wilhelms-Universität Bonn

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). Slides

Prof. Dr. Peter Koepke undertakes research in set theory and logic as a part of the Bonn Mathematical Logic Group. He earned his Ph.D. in 1984 and Habilitation in 1990 at Freiburg University. His specific research interests include axiomatic set theory, including infinitary combinatorics, forcing and core models, consistency strengths without the axiom of choice, large cardinals; constructibility theory, including ordinal computability theory and new fine structure theories; descriptive set theory and infinitary game theory; and general logic, including automated theorem proving and proof checking, such as in the NAPROCHE natural language proof-checking system.