The Structures Inside Turing Degrees of Recursively Enumerable Generic Sets

Jockusch and Ingrassia introduced notions of e-genericity, s-genericity and p-genericity for recursively enumerable sets in 1985 and 1980 respectively. It has been shown that there are many important properties of recursively enumerable generic sets and degrees. We have investigated the structures of wtt-degrees inside recursively enumerable p-generic Turing degrees and proved that every r.e. p-generic degree is noncontiguous. In this note, we

每个非零的 a∈ R/ M中不存在极小元(英文)

证明了给定任何非零的递归可枚举图灵度 a存在递归可枚举图灵度 c<a和 d∈M,使得 a≤ d∪ c.由此可以得到 :在每个非零 [a]∈ R∧ M中不存在极小元 ,即给定任何非可盖递归可枚举图灵度 a,存在一个递归可枚举图灵度 c<a,使得 [c]=[a].

Infimum Properties Differ in the Weak Truth-table Degrees and the Turing Degrees

We prove that there are non-recursive r.e.sets A and C with A<T C such that for every set F(?)T A,C∩F≡w(?).

相对可知度的构造

在本文中我们证明,对任何给定的两个r、e度b、e,若c≮b,则存在r、e度a≮b,使得c≮a∪b,即a相对于b,c的“不小于”关系(≮)具有可知性质。