报告：郑园园（University of Toronto)
题目：Parametrized theorems in Ramsey spaces
Abstract: Based on the work of Carlson and Simpson, Todorcevic axiomatized topological Ramsey spaces. There is an infinite-dimensional Ramsey-type theorem associated to each topological Ramsey space, e.g. the Ellentuck theorem and the Milliken theorem, from which one can derive the original Ramsey theorem and Hindman's theorem. We will have a brief introduction to the topological Ramsey spaces. We will then show how a parametrized Ramsey-type theorem gives us the result that certain ultrafilters are preserved under side-by-side Sacks forcing with countable support, inspired by the fact proved by Baumgartner and Laver that selective ultrafilters on the natural numbers are preserved under side-by-side Sacks forcing.