Turing Computations on Ordinals

Peter Koepke

Turing Computations on Ordinals

逻辑 2007-05-23 v1

作者: Peter Koepke

摘要

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.

关键词

set theory

引用

@article{arxiv.math/0502264,
  title  = {Turing Computations on Ordinals},
  author = {Peter Koepke},
  journal= {arXiv preprint arXiv:math/0502264},
  year   = {2007}
}

备注

Submitted to the Bulletin of Symbolic Logic, 20 pages

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