Universiteit van Amsterdam

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Institute for Logic, Language and Computation

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18 December 2001, Zuidelijk Interuniversitair Colloquium (ZIC), Dirk van Dalen

Speaker: Dirk van Dalen
Title: Brouwer's Continuity Principle
Date: 18 December 2001
Location: Room HG 6.96, TU Eindhoven

In 1918 Brouwer published a principle that was basic for the theory of choice sequences: the continuity principle, which says that all mappings from choice sequences of natural numbers to natural numbers are continuous. A foundational argument for the principle was not given. Since then a number of arguments have been put forward to provide a foundational basis for the principle. None of these have been absolutely successful to the degree that we accept the axioms for arithmetic. We will look into this matter and see what can be done. Also the case of the lawlike sequences is considered. Furthermore a pedestrian proof of the Kreisel-Lacombe-Shoenfield-Tscheitin theorem (all functions from recursive functionals to natural numbers are continuous) will be sketched, using a technique, now known as Ishihara's trick.

Please note that this newsitem has been archived, and may contain outdated information or links.