Mathematical Sciences: Formal Systems and Combinatorics

Timothy Carlson在有限和无限组合学中的工作为各种所谓的Ramsey定理提供了强大的统一推广。最简单的拉姆齐定理是这样的：如果空间中的六个点以所有可能的方式由直线段连接，并且每一段要么被涂成红色，要么被涂成绿色，那么总会有一个边相同颜色的完整三角形。这个定理已经以各种不同的方式被推广到难以辨认的程度，但所有这样的推广都被称为拉姆齐定理。它们在几何学、数论和其他领域有许多重要的结果，有统一的原理为这些推论提供经济的推导是非常有用的。将寻求这种性质的进一步结果。

Timothy Carlson's work in finite and infinite combinatorics provides powerful unifying generalizations of various so-called Ramsey theorems. The simplest Ramsey theorem is the following: if six points in space are connected in all possible ways by straight line segments and each segment is painted either red or green, then there will always be an entire triangle whose sides are of the same color. This theorem has been generalized beyond easy recognition in a variety of different ways, but all such generalizations are referred to as Ramsey theorems. They have a host of significant consequences in geometry and number theory and elsewhere, and it is very useful to have unifying principles which provide economical derivations for these corollaries. Further results of this nature will be sought.