The Jump Hierarchy in the Enumeration Degrees
نویسنده
چکیده
We show that all levels of the jump hierarchy are first order definable in the local structure of the enumeration degrees.
منابع مشابه
On the jump classes of noncuppable enumeration degrees
We prove that for every Σ2 enumeration degree b there exists a noncuppable Σ2 degree a > 0e such that b ′ ≤e a′ and a′′≤e b′′. This allows us to deduce, from results on the high/low jump hierarchy in the local Turing degrees and the jump preserving properties of the standard embedding ι : DT → De, that there exist Σ2 noncuppable enumeration degrees at every possible—i.e. above low1—level of the...
متن کاملNon-cuppable enumeration degrees via finite injury
We exhibit finite injury constructions of a high Σ2 enumeration degree incomparable with all intermediate ∆2 enumeration degrees, as also of both an upwards properly Σ2 high and a low2 noncuppable Σ 0 2 enumeration degree†. We also outline how to apply the same methods to prove that, for every Σ2 enumeration degree b there exists a noncuppable degree a such that b′ ≤ a′ and a′′ ≤ b′′, thus show...
متن کاملBadness and jump inversion in the enumeration degrees
This paper continues the investigation into the relationship between good approximations and jump inversion initiated by Griffith. Firstly it is shown that there is a Π2 set A whose enumeration degree a is bad—i.e. such that no set X ∈ a is good approximable—and whose complement A has lowest possible jump, in other words is low2. This also ensures that the degrees y ≤ a only contain ∆3 sets and...
متن کاملThe Jump Operator on the Ω-enumeration Degrees
The jump operator on the ω-enumeration degrees is introduced in [11]. In the present paper we prove a jump inversion theorem which allows us to show that the enumeration degrees are first order definable in the structureDω ′ of the ω-enumeration degrees augmented by the jump operator. Further on we show that the groups of the automorphisms of Dω ′ and of the enumeration degrees are isomorphic. ...
متن کاملDefinability via Kalimullin Pairs in the Structure of the Enumeration Degrees
We give an alternative definition of the enumeration jump operator. We prove that the class of total enumeration degrees and the class of low enumeration degrees are first order definable in the local structure of the enumeration degrees.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016