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

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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. ***