Mathematical Sciences: Geometrical Studies of Superstable Theories

Buechler教授在数理逻辑方面的研究是在 稳定性理论是模型论的一个分支。 近年来 几个一般的模型理论问题已经被系统地 通过稳定性等级体系进行处理。 即使问题 本身可能不涉及稳定理论的概念，考虑到 分别地，情况：Ω稳定的、超稳定的等，带来 大量的技术机器发挥作用。 这就是 Vaught猜想，由Shelah证明为ω-稳定 理论 下一步是考虑所有的超稳定理论， 但事实证明，这对在美国使用的方法来说太困难了。 Ω稳定的情况。 所需要的是一种分析， 敏感的方式，例如，秩α的集合是 拼凑在一起形成秩为α加1的集合。 布伊齐勒 将继续用几何方法来解决这个问题， 已经取得了显著的成果。

Professor Buechler's research in mathematical logic is in stability theory, a subfield of model theory. In recent years several general model-theoretic problems have been systematically approached via the stability hierarchy. Even though the problem itself may not involve stability-theoretic notions, considering separately the cases: omega-stable, superstable, etc., brings into play a mass of technical machinery. Such is the case for Vaught's conjecture, which was proved by Shelah for omega-stable theories. The next step is to consider all superstable theories, but this has proved too difficult for the methods used in the omega-stable case. What is required is an analysis which is sensitive to the way in which, e.g., sets of rank alpha are pieced together to form sets of rank alpha plus one. Buechler will continue with this geometrical approach to the problem, which has already yielded significant results.