Turing Computations on Ordinals
Logic
2007-05-23 v1
Abstract
We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length 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.
Keywords
Cite
@article{arxiv.math/0502264,
title = {Turing Computations on Ordinals},
author = {Peter Koepke},
journal= {arXiv preprint arXiv:math/0502264},
year = {2007}
}
Comments
Submitted to the Bulletin of Symbolic Logic, 20 pages