Theorie der Darstellungen und ihre Anwendungen
in der konstruktiven Analysis.


Christoph Kreitz.

PhD Thesis, Fernuniversität Hagen, 1984.   (German)


Abstract

We present an approach for a unified theory of effectivity on nondenumerable sets. It is based on a standard Type 2 theory of computability and continuity on F={f:N->N} and a theory of representations, i.e. mappings from F onto some set , which enable us to transfer computability concepts from F onto arbitary sets with cardinality not greater than that of the continuum. We study topological and recursion theoretical properties of representations as the continuity and computability models induced by them.
As an application show how to use these concepts as a foundation of a new kind of constructive analysis. We compare different representations of the real numbers and of the open subsets of the real numbers and investigate which of them are suitable for studying computability in analysis. In particular we consider constructive compactness and investigate the constructivity properties of the standard theorems about continuous functions on compact sets.

The thesis is written in German. Its contents are essentially covered by the following publications
- A unified approach to constructive and recursive analysis. Logic Colloquium Aachen, 1984.
- Theory of representations. Theoretical Computer Science, 1985.
- Representations of the real numbers and the open subsets of the set of real numbers. Annals of pure and applied logic, 1987.
- Compactness in constructive analysis revisited. Annals of pure and applied logic, 1987.


Not available online   Send an email to to receive a hard copy BACK
Back to overview of papers


Bibtex Entry

@PhDThesis{phd:Kreitz84a, author = "Christoph Kreitz", title = "{Theorie der Darstellungen und ihre Anwendungen in der konstruktiven Analysis}", school = "FernUniversit{\"a}t Hagen, FB Mathematik und Informatik", year = "1984" }