Turing Computations on Ordinals

Details Turing Computations on Ordinals Turing Computations on Ordinals

2005-02-13

arxiv.org/abs/math/0502264v1

Mathematics

Logic

Submitted to the Bulletin of Symbolic Logic, 20 pages

Scientific paper

We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length $\omega$ 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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