English

Computing sets from all infinite subsets

Logic 2020-11-09 v1

Abstract

A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the collection of introreducible sets is Π11\Pi^1_1-complete, so that there is no simple characterization of the introreducible sets; and that every introenumerable set has an introreducible subset.

Keywords

Cite

@article{arxiv.2011.03386,
  title  = {Computing sets from all infinite subsets},
  author = {Noam Greenberg and Matthew Harrison-Trainor and Ludovic Patey and Dan Turetsky},
  journal= {arXiv preprint arXiv:2011.03386},
  year   = {2020}
}

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30 pages