Welcome to the website of the Bonn-Amsterdam research group "Infinitary combinatorics without the axiom of choice".
In the presence of the axiom of choice many infinitary combinatorial principles motivated by general model theory or cardinal arithmetic are so strong that their consistency strengths with respect to the standard set theoretic axiom system ZFC cannot be exactly determined by current forcing and core model techniques. Weakening or omitting the choice assumptions can weaken principles so that their consistency strengths become "tractable" by existing techniques. This research project carries out detailed consistency studies on a wide spectrum of combinatorial principles without the (full) axiom of choice, including versions of Chang's conjecture, Rowbottom cardinals, accessible partition cardinals, and cardinal arithmetic for singular cardinals. Our project is based on an intense collaboration between set theorists at Amsterdam, Bonn, and New York.