Dag Normann

Lecture Notes
Research Interests
Slides of scientific talks


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

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

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.


Fall 2008: MAT4300 - Measure and integration theory

Lecture Notes

Logikk og Mengdelære (in Norwegian).
Graduate course on computability theory and model theory
Lectures on type theory and lambda calculus in Norwegian.

Past and current research Interests

Measurability in Polish and analytic spaces (Master Thesis).
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.

Slides of scientific talks

CiE2008: Slides and full beamer presentation.


M. Sc. student Håkon Briseid.

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

The complete bibliography


For published papers, the links are not to the final versions.
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. Exact real number computations relative to hereditarily total functionals
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.