## RESTRICTED JUMP INTERPOLATION IN THE D.C.E. DEGREES (2009)

### BibTeX

@MISC{Jockusch09restrictedjump,

author = {Carl G. Jockusch and Angsheng Li},

title = {RESTRICTED JUMP INTERPOLATION IN THE D.C.E. DEGREES},

year = {2009}

}

### OpenURL

### Abstract

It is shown that for any 2-computably enumerable Turing degree l, any computably enumerable degree a, and any Turing degree s, if l ′ = 0 ′, l < a, s ≥ 0 ′ , and s is c.e. in a, then there is a 2-computably enumerable degree x with the following properties: (1) l < x < a, and (2) x ′ = s. 1

### Citations

72 | Soare, Recursively Enumerable Sets and Degrees - I - 1987 |

46 | On the degrees less than 0 - Sacks - 1963 |

37 | The upper semi-lattice of degrees of recursive unsolvability - Kleene, Post - 1954 |

36 | The recursively enumerable degrees are dense - Sacks - 1964 |

28 | Interpolation and embedding in the recursively enumerable degrees - Robinson - 1971 |

27 | A criterion for completeness of degrees of unsolvability - Friedberg - 1957 |

15 |
Soare, The d.r.e. degrees are not dense
- Cooper, Harrington, et al.
- 1991
(Show Context)
Citation Context ...ly enumerable degree a, and any Turing degree s, if l ′ = 0 ′ , l < a, s ≥ 0 ′ , and s is c.e. in a, then there is a 2-computably enumerable degree x with the following properties: (1) l < x < a, and =-=(2)-=- x ′ = s. 1 Introduction The topic of inverting the Turing Jump in the Turing degrees started in the 1950’s. Following the pioneering work of Kleene and Post (1954), Friedberg (1957) provided a comple... |

8 | Jump restricted interpolation in the recursively enumerable degrees - Robinson - 1971 |

6 |
There is no low maximal d.c.e
- Arslanov, Cooper, et al.
- 2004
(Show Context)
Citation Context ...ree l, any computably enumerable degree a, and any Turing degree s, if l ′ = 0 ′ , l < a, s ≥ 0 ′ , and s is c.e. in a, then there is a 2-computably enumerable degree x with the following properties: =-=(1)-=- l < x < a, and (2) x ′ = s. 1 Introduction The topic of inverting the Turing Jump in the Turing degrees started in the 1950’s. Following the pioneering work of Kleene and Post (1954), Friedberg (1957... |

6 | A minimal degree not realizing least possible jump - SASSO - 1974 |

3 | A hierarchy of sets, Part I', Algebra i Logika 7 - ERSHOV - 1968 |

2 | On Lachlan's major subdegree problem, to - Cooper, Li - 1989 |

2 | A hierarchy of sets, Part II', Algebra i Logika 7 - ERSHOV - 1968 |

1 | On degrees of recursive unsolvability, Ann. of Math. (2) 64 - Spector - 1956 |