Mathematical Sciences: Geometrical Stability Theory

Steven A. Buechler的研究项目是稳定性理论， 模型论的一个分支。 近年来，几种通用型号- 理论问题已系统地探讨了通过 稳定性层次 即使问题本身可能 涉及稳定性理论的概念，分别考虑 情况：Ω稳定、超稳定等，发挥了大量的 技术机械。 这就是Vaught的猜想， 这是由谢拉证明的ω稳定理论。 下一 第一步是考虑所有的超稳定理论，但这已经证明 太难了 Buechler将通过以下方式解决这个问题： 将超稳定理论按照其 “几何”属性。 要考虑的第一种情况是， 宇宙有等级1的希拉。 Buechler已经取得了进展， 这个问题

Steven A. Buechler's research project 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 with Vaught's conjecture, which was proved by Shelah for omega-stable theories. The next step is to consider all superstable theories, but this has proven to be too difficult. Buechler will approach this problem by separating the superstable theories according to their "geometrical" properties. The first case to consider is when the universe has Shelah rank 1. Buechler has already made progress on this problem.