Degrees of Nonrecursive Presentability

Array Nonrecursive Degrees and Genericity

A class of r.e. degrees, called the array nonrecursive degrees, previously studied by the authors in connection with multiple permitting arguments relative to r.e. sets, is extended to the degrees in general. This class contains all degrees which satisfy a 00 > (a 0 0) 0 (i.e. a 2 GL 2) but in addition there exist low r.e. degrees which are array nonrecursive (a.n.r.). Many results for GL 2 deg...

Effective Reducibilities on Structures and Degrees of Presentability

In this survey paper we consider presentations of structures in admissible sets and some effective reducibilities between structures and their degrees of presentability. Degrees of Σ-definability of structures, as well as degrees of presentability with respect to different effective reducibilities, are natural measures of complexity which are total, i.e. defined for any structure. We also consi...

Optimization of Nonrecursive Queries

State-of-the-art optimization approaches for relational database systems, e.g., those used in systems such as OBE, SQL/DS, and commercial INGRES. when used for queries in non-traditional database applications, suffer from two problems. First, the time complexity of their optimization algorithms, being combinatoric, is exponential in the number of relations to be joined in the query. Their cost ...

Design Problems for Nonrecursive

On Mass Problems of Presentability

We consider the notion of mass problem of presentability for countable structures, and study the relationship between Medvedev and Muchnik reducibilities on such problems and possible ways of syntactically characterizing these reducibilities. Also, we consider the notions of strong and weak presentability dimension and characterize classes of structures with presentability dimensions 1. 1 Basic...