What's the difference between rectangles and squares?

יום א', 24/11/2013 - 14:00

Ramsey's theorem states that for every symmetric partition of the square X2 of an infinite set X into finitely many cells, there would be a cell that covers the square Y2 of some infinite subset Y of X. Erdos and his collaborators considered various generalization of Ramsey's statement (replacing "infinite" with "uncountable", "finitely many" with "countably many", "square" with "rectangle"), and demonstraed the (consistent) failure of many of them. In this talk, we shall present this line of research, with the goal of elucidating the difference between rectangles and squares.