Galvin's Problem In Higher Dimensions

Seminar
Speaker
Ido Feldman (BIU)
Date
12/05/2022 - 17:00 - 15:00Add to Calendar 2022-05-12 15:00:00 2022-05-12 17:00:00 Galvin's Problem In Higher Dimensions In 1970's Galvin conjectured that for all colorings of the reals there is a subset H of the reals homeomorphic to the rational numbers that gets at most two colors. i.e. the 2-dimensional Ramsey degree of the rational with respect to the reals is 2. Baumgartner proved that if we consider any infinite countable Hausdorff space X then there is a coloring with \omega many colors, which takes all its values on subsets homeomorphic to \mathbb{Q}. In paper from 2018 Raghavan and Todorcevic showed that assuming existance of Woodin cardinal the 2-dimensional Ramsey degree of \mathbb{Q} within respect to the class of all uncountable sets is 2. In this talk we give a result of Raghavan and Todorcevic in higher dimensions which is that there is no generalization of their previous theorem to dimension 3 and higher. Building 305, Room 133 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Building 305, Room 133
Abstract

In 1970's Galvin conjectured that for all colorings of the reals there is a subset H of the reals homeomorphic to the rational numbers that gets at most two colors. i.e. the 2-dimensional Ramsey degree of the rational with respect to the reals is 2. Baumgartner proved that if we consider any infinite countable Hausdorff space X then there is a coloring with \omega many colors, which takes all its values on subsets homeomorphic to \mathbb{Q}. In paper from 2018 Raghavan and Todorcevic showed that assuming existance of Woodin cardinal the 2-dimensional Ramsey degree of \mathbb{Q} within respect to the class of all uncountable sets is 2. In this talk we give a result of Raghavan and Todorcevic in higher dimensions which is that there is no generalization of their previous theorem to dimension 3 and higher.

Last Updated Date : 10/05/2022