On Kalimullin pairs

Definability 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.

Kalimullin Pairs of Σ2 Ω-enumeration Degrees

We study the notion of K-pairs in the local structure of the ωenumeration degrees. We introduce the notion of super almost zero sequences and investigate their structural properties. The study of degree structures has been one of the central themes in computability theory. Although the main focus has been on the structure of the Turing degrees and its local substructure, of the degrees below th...

The Least ∑-jump Inversion Theorem for n-families

Studying the Σ-reducibility of families introduced by [Kalimullin and Puzarenko 2009] we show that for every set X T ∅′ there is a family of sets F which is the Σ-least countable family whose Σ-jump is Σ-equivalent to X ⊕X. This fact will be generalized for the class of n-families (families of families of . . . of sets).

Total Degrees and Nonsplitting Properties of Enumeration Degrees

Algorithmic reducibilities of algebraic structures

Using admissibility for a computable model theory for uncountable structures