We prove a jump inversion theorem for the enumeration jump and a minimal pair type theorem for the enumeration reducibilty. As an application some results of Selman, Case and Ash are obtained.

The jump operator on the Ï‰-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 orderâ€¦ (More)

In the paper we introduce and study the uniform regular enumerations for arbitrary recursive ordinals. As an application of the technique we obtain a uniform generalization of a theorem of Ash and aâ€¦ (More)

The paper is devoted to the study of Markerâ€™s extensions of sequences of countable structures. In the first part of the paper definability properties of the Markerâ€™s extension are investigated. Theâ€¦ (More)

The main result proved in the paper is that on every recursive structure the intrinsically hyperarithmetical sets coincide with the relatively intrinsically hyperarithmetical sets. As a side eeect ofâ€¦ (More)

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 ,â€¦ (More)