Turing Computations on Ordinals

Peter Koepke

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Turing Computations on Ordinals

Peter Koepke

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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 Goedel's constructible universe L. This characterization can be used to prove the generalized continuum hypothesis in L.

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BibTeX RIS

Peter Koepke. 2005-02-13. Turing Computations on Ordinals. https://arxiv.org/abs/math/0502264

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