Towards a theory of representations.

Christoph Kreitz, Klaus Weihrauch.

In G. Wechsung, ed., 2nd Frege Conference, pp. 73-79, Akademie Verlag, 1984.


This paper presents the concept of representations as a foundation for a unified Type 2 computability theory. Its basic idea is that real world computers cannot operate on abstract elements of a set M but only on names. We have chosen the set F of sequences of natural numbers as a standard set of names and have defined computability on F explicitly. Computability on other sets M can then be derived from computability on F by means of representations, i.e. (partial) mappings from F onto M.
Computable functions turn out to be continuous in general and in most cases functions that are not computable are not even continuous. Hence topological considerations are fundamental for Type 2 theory and continuity w.r.t. representations are also studied.

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Bibtex Entry

@InProceedings{inp:KreitzWeihrauch84b, author = "Christoph Kreitz and Klaus Weihrauch", title = "Towards a theory of representations", booktitle = "2$^{nd}$ Frege Conference", year = 1984, pages = "73--79", editor = "G. Wechsung", publisher = "Akademie Verlag", address = "Berlin" }