Mathematical Sciences: Geometrical Stability Theory

Steven a . Buechler的研究项目是稳定性理论，这是模型理论的一个分支。近年来，利用稳定性层次理论系统地研究了一些一般的模型理论问题。尽管问题本身可能不涉及稳定性理论概念，但单独考虑ω -稳定、超稳定等情况，就需要使用大量的技术机制。这就是沃特猜想的例子，这个猜想被希拉证明为-稳定理论。下一步是考虑所有的超稳定理论，但这已经被证明是太困难了。Buechler将通过根据它们的“几何”性质分离超稳定理论来解决这个问题。要考虑的第一种情况是宇宙中希拉排名第一。比希勒已经在这个问题上取得了进展。

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.