Infinitary combinatorics without the axiom of choice

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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 however weaken principles so that their consistency strengths become "tractable" by existing techniques. The research project /Infinitary Combinatorics without the Axiom of Choice/ will carry 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. The project is based on an intense collaboration between set theorists at Amsterdam, Bonn, and New York. Support is requested for a Ph.D. position at Bonn to be filled by Ioanna Dimitriou. Dimitriou will also coordinate the compilation and publication of comprehensive lecture notes evolving from this project.