Computable Lipschitz归约(简记为cl-归约)是强Turing归约，即给定变量,其用函数对应为增加某个常数[DHL01]。作为比较实数随机性的归约工具，cl-归约由新西兰的Downey，美国的Hirschfieldt,Lafort等专家提出，其对应的cl-度内实数具有相同的随机程度。所以，在cl-归约下，度的结构，尤其是c.e.实数对应的度的结构,及利用cl-归约下性质刻画随机实数对随机性理论具重要意义。国内外随机性理论研究方面诸多专家对以上的问题展开了丰富的研究，见文献[BL06]等。另一方面，c.e.集合在cl-归约（ibT归约-特殊的cl-归约）下对应的度的结构，其特殊性质，如非稠密等，促使可计算理论学者关注对cl-归约下c.e.集合度结构的研究。本课题拟从以上两方面来研究cl-归约的性质。

Computable Lipschitz(cl-) reducibility is a strengthening of weak truthtable reducibility, namely computations where the use on the oracle on argument n is n + c for some constant c, was suggested as a possible measure of relative.randomness by Downey，Hirschfieldt,Lafort[DHL01].. Having defined cl-reducibility we can consider the structure of the induced degrees.The cl-degrees are the equivalence classes under cl-reducibility..Notice that they either contain only random reals or only non-random reals. Since cl-reducibility is a strengthening of weak truth table reducibility, the structure of cl-degrees is interesting from the computation complexity. So the structure of cl-degrees of c.e. reals is interesting from randomness theory. Some concerned results are given in [BL06]，[BL07]etc.. Although cl-reducibility is a strengthening of weak truth table reducibility, the structure of cl-degrees of c.e. sets is different from the wtt-degrees and Turing degrees. For instance, the cl-degrees( or ibT-degrees) of c.e. sets are not dense. So the structure of cl-degrees is interesting from computation theory. .In our project, we will analyze the properties of the cl-reducibilty, to explore the structure of cl-degrees of c.e. reals (or sets).