Mathematical Sciences: Set Theory: Sets of Real Numbers and Infinite Games

9505375 Bartoszynski、Bartoszynski和Schepers的研究是集合论。他们的一些问题是众所周知的，而另一些问题则是最近的工作中出现的。其中许多问题的一个共同主题是在强迫结构和归纳结构之间建立联系。另一个潜在的目标是用无限博弈的语言来表达集合的各种性质。预计模型理论、强迫理论、组合集合论和博弈论的概念将在本研究中发挥重要作用。他们的研究植根于康托、豪斯多夫、戈德尔和科恩的工作，他们计划的研究将涉及无限的概念，以及这些概念在现代数学领域中的一些微妙方式。他们探索的问题特别集中在被称为“基础”的数学领域，答案可能超出了它的界限。本质上，他们的方法将现代逻辑和博弈论的先进方法应用于基础和实际分析的交叉点上的问题。***

9505375 Bartoszynski Bartoszynski and Scheepers' research is in set theory. Some of their problems are well-known, while others have arisen from more recent work. One common theme for many of these problems lies in establishing a link between forcing and inductive constructions. Another underlying goal is to express various properties of sets in the language of infinite games. It is expected that notions from model theory, forcing theory, combinatorial set theory and game theory will play a significant role in this research. With its roots in the work of Cantor, Hausdorff, Godel and Cohen, their projected research will deal with the notions of the infinite and some subtle ways in which these notions manifest themselves in areas of modern mathematics. The questions they explore are specifically focused on that area of mathematics known as "foundations," with answers that potentially extend beyond its boundaries. In essence, their approach will apply the advanced methods of modern logic and game theory to problems that lie in the intersection of foundations and real analysis. ***