Big Ramsey Degrees of the Pseudotree
报告专家：David Chodounský（Institute of Mathematics of the Czech Academy of Sciences）
报告时间：9月21日（星期一）下午15:00-17:00
报告地点：国家天元数学西南中心516
报告摘要：
We say that structure A has big Ramsey degree n in structure X if for every coloring of substructures of X which are isomorphic to A by finitely many colors there is a substructure Y of X which is isomorphic to X, such copies of A in Y are colored by at most n-many colors. Ramsey's theorem says that every finite set (without any structure) has big Ramsey degree 1 in the set of natural numbers. Baumgartner proved that for every finite linear order A the big Ramsey degree of A in the set of rationals is finite; this is phrased as ‘rationals do have finite big Ramsey degrees’.
We are interested in big Ramsey degrees of finite trees in the pseudotree -- the universal countable homogeneous meet tree. It turns out that finite tree A has a finite big Ramsey degree in the pseudotree iff A is a chain. I will sketch the main steps of the argument.
Joint work with N. Dobrinen, M. Eskew, and T. Weinert.
专家简介：
Dr. David Chodounský is a researcher at the Institute of Mathematics of the Czech Academy of Sciences and an external lecturer at Charles University in Prague. His research focuses on set theory, forcing, Ramsey theory, and infinitary combinatorics. His work has appeared in leading international journals, including the Journal of the European Mathematical Society, Annals of Pure and Applied Logic, Israel Journal of Mathematics, and Combinatorica.
邀请人：何家亮
