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Turing Computations On Ordinals

Published online by Cambridge University Press:  15 January 2014

Peter Koepke
Peter Koepke*
Affiliation:
Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität, Beringstraße 1, D-53115 Bonn, Germany. E-mail: [email protected]
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Abstract

We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite set of ordinal parameters if and only if it is an element of Gödel's constructible universe L. This characterization can be used to prove the generalized continuum hypothesis in L.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 11 , Issue 3 , September 2005 , pp. 377 - 397
Copyright
Copyright © Association for Symbolic Logic 2005

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References

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