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

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Veröffentlicht in:Transactions of the American Mathematical Society 2021-11, Vol.374 (11), p.8131-8160
Hauptverfasser: Greenberg, Noam, Harrison-Trainor, Matthew, Patey, Ludovic, Turetsky, Dan
Format: Artikel
Sprache:eng
Schlagworte:
Logic
Mathematics
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Zusammenfassung: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 \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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8468