Computability in Europe 2008
Logic and Theory of Algorithms

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Invited Plenary Talk:
50 years of continuous functionals

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Speaker: Dag Normann


Approximately 50 years have passed since Kleene and Kreisel independently defined the almost equivalent hierarchies of the countable and the continuous functionals, and these functionals have been studied by small, but dedicated groups of researchers ever since.

In many respects, the research community interested in computations in higher type objects forms an elementary substructure of the CiE community as a whole.

In this community researchers from traditional generalized computability theory and from theoretical computer science meet, exchange ideas, solve each other problems and find new areas of applications. We will give some examples. This will also be reflected in the special session on the subject.

In this talk we will review the original motivations and a few results from the first 20 years and draw the lines via the partial continuous and the sequential functionals to the research of today.

The talk will not be technical.

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