Generalized Baire spaces - definability and paradoxical sets

这个项目研究实数的“悖论”集，或者更一般的高阶Baire空间的“悖论”子集，它们可以从底层空间的良好秩序中构造出来。一个原型例子是哈默尔基，即实数的基，被解释为有理数上的向量空间。我们的目标是构建模型，其中存在这些类型的集合，但不允许各自空间的良好排序。

This project studies "paradoxical" sets of reals, or more generally "paradoxical" subsets of higher Baire spaces, which may be constructed from a well-order of the underlying space. A prototype example is a Hamel basis, i.e., a basis for the reals, construed as a vector space over the rationals. We aim to construct models in which those types of sets exist but which do not admit a well-ordering of the respective space.