Covering the Baire space by families which are not finitely dominating

在广义Baire空间上分离多个局部化基数

Separating Many Localisation Cardinals on the Generalised Baire Space

本文在广义Baire空间中构造 $\kappa$ 个基数函数及其局部化数，并用保持共尾性的乘积力迫证明它们可同时取 $\kappa$ 以上任意不同基数，解决已有开放问题。

The Hurewicz covering property and slaloms in the Baire space

According to a result of Kocinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover to obtain a groupable cover of the space. We simplify the characterization further by omitting the need to consider sequences of covers: A set of reals $X$ satisfies the Hurewicz property if, and only if, each large open cover of $X$ contains a groupable subcover. This solves in the affirmative a problem of Scheepers. The proof uses a rigorously justified a…

Laver Trees in the Generalized Baire Space

We prove that any suitable generalization of Laver forcing to the space $ κ^κ$, for uncountable regular $κ$, necessarily adds a Cohen $κ$-real. We also study a dichotomy and an ideal naturally related to generalized Laver forcing. Using this dichotomy, we prove the following stronger result: if $ κ^{<κ}=κ$, then every $<κ$-distributive tree forcing on $κ^κ$ adding a dominating $κ$-real which is the image of the generic under a continuous function in the ground model, adds a Cohen $κ$-real. This is a contribution to the study of generalized Baire spaces and answers a question from arXiv:1611.08…

有界广义 Baire 空间上的基数特征

Cardinal Characteristics on Bounded Generalised Baire Spaces

本文研究强不可达 $κ$ 下广义 Baire 空间有界子空间中的支配、最终差、局部化与反局部化基数特征，分析其非平凡参数、相互关系及广义 Cichoń 图，并证明参数可一致导致不同基数。

Closed Choice and a Uniform Low Basis Theorem

We study closed choice principles for different spaces. Given information about what does not constitute a solution, closed choice determines a solution. We show that with closed choice one can characterize several models of hypercomputation in a uniform framework using Weihrauch reducibility. The classes of functions which are reducible to closed choice of the singleton space, of the natural numbers, of Cantor space and of Baire space correspond to the class of computable functions, of functions computable with finitely many mind changes, of weakly computable functions and of effectively Bore…

论无需选择公理的强公平社会福利序

On Strongly-equitable Social Welfare Orders Without the Axiom of Choice

本文研究强公平且有限匿名的社会福利序（SEA），证明其存在蕴含不可勒贝格测度的实数集存在，但不蕴含自然数上非主超滤子的存在，并运用几何集合论技术解决开放问题。