The thesis consists of four sections . in section one , we introduce some background of the topic , in section two we review some basic and recent results about the structure and hierarchies of the computably enumerable degrees which are closely related to our topic - the algebraic structure of the plus cupping turing degrees , in section three , we outline the basic principles of the priority tree argument , one of the main frameworks and tools of theorem proving in computability theory , and in section four , we prove a new result concerning the algebraic structure of the plus cupping turing degrees that there exist two computably enumerable degrees a , b such that a , b ? pc , and the join a v b of a and b is high 本篇论文分为4个部分：第一部分介绍了这个领域的一些背景知识；第二部分主要回顾了前人在研究可计算枚举度的结构和层谱时所取得的一些基本和最新结果，这些结果与我们的主题?加杯图灵度的代数结构密切相关；在第三部分中，我们概要的描述了优先树方法的基本原理，此方法是可计算性理论中定理证明的一个重要框架和工具；第四部分证明了一个加杯图灵度代数结构的新结果：存在两个可计算枚举度a ， b ，满足a ， b pc ，而且a和b的并a b是一个高度。
