Density of the Cototal Enumeration Degrees
نویسندگان
چکیده
We prove that the cototal enumeration degrees are exactly the enumeration degrees of sets with good approximations, as introduced by Lachlan and Shore [17]. Good approximations have been used as a tool to prove density results in the enumerations degrees, and indeed, we prove that the cototal enumerations degrees are dense.
منابع مشابه
On Cototality and the Skip Operator in the Enumeration Degrees
A set A ⊆ ω is cototal if it is enumeration reducible to its complement, A. The skip of A is the uniform upper bound of the complements of all sets enumeration reducible to A. These are closely connected: A has cototal degree if and only if it is enumeration reducible to its skip. We study cototality and related properties, using the skip operator as a tool in our investigation. We give many ex...
متن کاملConnected Cototal Domination Number of a Graph
A dominating setD ⊆ V of a graphG = (V,E) is said to be a connected cototal dominating set if 〈D〉 is connected and 〈V −D〉 6= ∅, contains no isolated vertices. A connected cototal dominating set is said to be minimal if no proper subset of D is connected cototal dominating set. The connected cototal domination number γccl(G) of G is the minimum cardinality of a minimal connected cototal dominati...
متن کاملEmbedding countable partial orderings in the enumeration degrees and the ω-enumeration degrees
One of the most basic measures of the complexity of a given partially ordered structure is the quantity of partial orderings embeddable in this structure. In the structure of the Turing degrees, DT , this problem is investigated in a series of results: Mostowski [15] proves that there is a computable partial ordering in which every countable partial ordering can be embedded. Kleene and Post [10...
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 کامل