## Dedicated to Professor GΓΌnter Asser on the occasion of his eightieth birthday We introduce and study certain classes of optimization problems over the real numbers. The classes are defined by logical means, relying on metafinite model theory for so called R-structures (see [12,11]). More precis
The Arithmetical Hierarchy of Real Numbers
β Scribed by Xizhong Zheng; Klaus Weihrauch
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 225 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We extend the hierarchy defined in [5] to cover all hyperarithmetical reals. An intuitive idea is used or the definition, but a characterization of the related classes is obtained. A hierarchy theorem and two fixed point theorems (concerning computations related to the hierarchy) are pr
A real number is recursively approximable if there is a computable sequence of rational numbers converging to it. If some extra condition to the convergence is added, then the limit real number might have more effectivity. In this note we summarize some recent attempts to classify the recursively ap