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Much recent research on Turing degrees has focused on the overall structure of the set of Turing degrees and the set of Turing degrees containing recursively enumerable sets.  A deep theorem of Shore and Slaman (1999) states that the function mapping a degree x to the degree of its Turing jump is definable in the partial order of the Turing degrees.  A recent survey by Ambos-Spies and Fejer (2006) gives an overview of this research and its historical progression.

Much recent research on Turing degrees has focused on the overall structure of the set of Turing degrees and the set of Turing degrees containing recursively enumerable sets.  A deep theorem of Shore and Slaman (1999) states that the function mapping a degree x to the degree of its Turing jump is definable in the partial order of the Turing degrees.  A recent survey by Ambos-Spies and Fejer (2006) gives an overview of this research and its historical progression.

最近很多关于图灵度的研究都集中在图灵度集的总体结构和包含递归可枚举集的图灵度集上。朔尔和斯拉曼(1999)的一个深刻定理指出，映射一个度x到其图灵跳度的函数可以按照图灵度的偏序定义。安博斯-斯皮尔斯和费耶尔(2006)最近的一项调查给出了这项研究及其历史进展的概述。

最近很多关于图灵度的研究都集中在图灵度集的总体结构和包含递归可枚举集的图灵度集上。索尔和斯拉曼(1999)的一个深刻定理指出，映射一个度x到其图灵跳度的函数可以按照图灵度的偏序定义。安博斯-斯皮尔斯和费耶尔(2006)最近的一项调查给出了这项研究及其历史进展的概述。

===Other reducibilities===

===Other reducibilities===