Defining the degree of categoricity of a computable structureM to be the least degree d for whichM is d-computably categorical, we investigate which Turing degrees can be realized as degrees ofâ€¦ (More)

This paper (see Theorem 6 below) describes general conditions under which relative splittings and specified diamond embeddings are derivable in the local structure of the enumeration degrees. In soâ€¦ (More)

Let N be a countable algebraic structure in a finite language Î£ (where the equality symbol = belongs to Î£) whose universe is a subset of Ï‰. We denote via D(N ) the set of all atomic sentences andâ€¦ (More)

Under degree spectrum of a countable algebraic structure, we understand the class of all Turing degrees that compute one of its isomorphic copies. It was shown in [2] that the classes LowÎ±+1 ofâ€¦ (More)

In this paper we introduce a hierarchy of families which can be derived from the integers using countable collections. This hierarchy coincides with the von Neumann hierarchy of hereditary countableâ€¦ (More)

Studying the Î£-reducibility of families introduced by [Kalimullin and Puzarenko 2009] we show that for every set X T âˆ…â€² there is a family of sets F which is the Î£-least countable family whose Î£-jumpâ€¦ (More)