Teaching

Lecture Notes

Research Interests

Slides of scientific talks

Students

e-prints

Department of Mathematics, The University of Oslo, Blindern, N-0316 Oslo, Norway

Private Adress: Damveien 5, N-1415 Oppegård, Norway

Telephone:

Private: (+ 47) 66 99 35 68

Mobile: (+47) 41 25 02 05

Work: (+ 47) 22 85 59 53

Telefax: (+ 47) 22 85 43 49

e-mail: dnormann@math.uio.no

Associated with the Logic Group at the University of Oslo.

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Recursion in normal functionals and set recursion.

Recursion over the Kleene-Kreisel total continuous functionals.

Dilators, ptykes and such things.

Transfinite hierarchies of algebraic domains with totality, with applications.

Totality as a concept not well understood.

Computability and continuity in higher types over the reals and other topological spaces.

Top.

Ph.D. students Petter Køber and (secondary advisor) Mathias Barra.

Top.

When the tittle of the paper is the link, the format is postscript.

*A rich hierarchy of functionals of finite types* in pdf-format.

* Applications of the Kleene-Kreisel Density Theorem to Theoretical
Computer Science* in pdf-format.

*On sequential functionals of type 3* in
pdf-format.

Has appeared in *Mathematical Structures in Computer Science*.

*Computing with functionals - computability theory or computer science?*
in pdf-format.

Has appeared in *Bulletin of Symbolic Logic*.

*Om mulige og tilsynelatende umulige programmeringsoppgaver* i pdf-format.

(In Norwegian) Has appeared in NORMAT.

*Comparing hierarchies of total functionals* as a postscript- or as an uppdated pdf-file.

Has appeared in *Logical Methods in Computer Science*.

*Definability and reducibility in higher types over the reals* as a postcript- or pdf- file.

Has appeared in *Theoretical Computer Science*

Limit spaces and transfinite types

(Joint with Geir Waagbø.)

Has appeared in *Archives for Mathematical Logic*

*The computational power of M-ω* in postcripts-format.

(Joint with Christian Rørdam)

Has appeared in * Mathematical Logic Quarterly*

The continuous functionals of finite types over the reals

Has appeared in the proccedings of the first international symposium
on domain theory, Shanghai 1999.

Continuity, proof systems and the
theory of transfinite computations

Has appeared in *Archives for mathematical Logic*

Computability over the partial continuous functionals

Has appeared in *Journal of Symbolic Logic*

Categories of domains with totality

The paper has been revised and slimmed down, but
was never submitted for publication.

A Mahlo-universe of effective domains with totality

A slightly revised version is also available.

Has appeared in the proceedings of Logic Colloquium '97

Representation theorems for transfinite computability and definability

Has appeared in *Arcives for mathematical Logic*

Last revision: 18/11-08.