Mathematical Sciences: Recursive Model Theory

Knight打算继续研究递归中的问题， 模型理论，并分析组织和思考的方法 嵌套的优先级参数。 现在有几个这样的 方法：“工人”的方法，由哈灵顿，两个 “阿尔法系统”的版本（均由Ash开发）和一种方法 Lemmp和Lerman。 工人的方法和原来的 阿尔法系统都产生了相当多的结果， 递归模型理论 Knight有一个关于工人的元定理，类似于Ash 证明了他最初的阿尔法系统，除了没有那么多是 假定为r.e.，条件也更加复杂。 奈特希望简化并改进元定理， 工人 在奈特的元定理中，正如在阿什的原始 元定理，在底层产生的对象是递归的。 阿什的新阿尔法系统（比旧的更简单），以及 Lemmp和Lerman设计用于产生r.e.物体 屁股了. 递归模型理论存在着许多问题 （存在群的递归表示等），以及 就像在递归理论中一样，这些新方法应该产生 结果 递归理论作为一个课题的基础 数学的动机是希望将 可以通过算法计算的。 该算法不需要是 实际的，但它必须存在，并在原则上终止后， 一些有限的步骤。

Knight intends to continue to work on problems in recursive model theory, and to analyze methods for organizing and thinking about nested priority arguments. There are now several such methods: the method of "workers", developed by Harrington, two versions of "alpha-systems", both developed by Ash, and a method of Lemmp and Lerman. The method of workers and the original alpha-systems have each yielded quite a number of results in recursive model theory. Knight has a metatheorem for workers, similar to the one Ash proved for his original alpha-systems, except that not so much is assumed to be r.e., and the conditions are more complicated. Knight hopes both to simplify and to improve the metatheorem for workers. In Knight's metatheorem, as in Ash's original metatheorem, the object produced on the bottom is recursive. Ash's new alpha-systems (simpler than the old), and the method of Lemmp and Lerman, are designed to produce an r.e. object on the bottom. There are many problems in recursive model theory (existence of recursive presentations of groups, etc.), as well as in recursion theory, on which these new methods ought to yield results. Recursion theory as a topic in the foundations of mathematics is motivated by a desire to formalize the property of being computable by an algorithm. The algorithm need not be a practical one, but it must exist and terminate in principal after some finite number of steps.