Infinitary combinatorics without the axiom of choice

在选择公理的存在下，许多由一般模型论或基数算法驱动的无穷组合原理是如此强大，以至于它们相对于标准集合论公理系统ZFC的一致性强度不能被当前的强迫和核心模型技术准确地确定。然而，弱化或省略选择假设可能会削弱原则，从而使它们的一致性强度通过现有技术变得“容易处理”。研究项目/没有选择公理的无限组合/将对没有(完全)选择公理的广泛的组合原理进行详细的一致性研究，包括张氏猜想的版本、行底基数、可访问的分拆基数和奇数基数的基数算术。该项目是基于阿姆斯特丹、波恩和纽约的集合理论家之间的密切合作。波恩的一个博士职位将由Ioanna Dimitriou填补，请求提供支助。迪米特里欧还将协调编写和出版从该项目演变而来的综合讲稿。

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.