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arXiv · 2011.03386

Computing sets from all infinite subsets

Noam Greenberg·Matthew Harrison-Trainor·Ludovic Patey·Dan Turetsky
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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 $\Pi^1_1$-complete, so that there is no simple characterization of the introreducible sets; and that every introenumerable set has an introreducible subset.

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Noam Greenberg, Matthew Harrison-Trainor, Ludovic Patey, Dan Turetsky. 2020-11-06. Computing sets from all infinite subsets. https://arxiv.org/abs/2011.03386

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