Computing sets from all infinite subsets

Computing sets from all infinite subsets

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\boldsymbol {\Pi }^1_1...

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Veröffentlicht in:Transactions of the American Mathematical Society 2021-08, Vol.374 (11), p.8131-8160
Hauptverfasser: Greenberg, Noam, Harrison-Trainor, Matthew, Patey, Ludovic, Turetsky, Dan
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container_issue 11
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container_title Transactions of the American Mathematical Society
container_volume 374
creator Greenberg, Noam
Harrison-Trainor, Matthew
Patey, Ludovic
Turetsky, Dan
description 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\boldsymbol {\Pi }^1_1-complete, so that there is no simple characterization of the introreducible sets; and that every introenumerable set has an introreducible subset.
doi_str_mv 10.1090/tran/8468
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Research article
title Computing sets from all infinite subsets
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