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Every introenumerable set contains a uniformly introreducible subset
Abstract
We prove that every infinite introenumerable set contains an infinite uniformly introreducible subset, answering both parts of Question 1.7 of Greenberg, Harrison-Trainor, Patey, and Turetsky affirmatively. Moreover, a single procedure computes the original set from every infinite subset of the selected set. The proof combines the uniformization and refinement results of these authors with Ramsey-theoretic methods and a canonical reconstruction argument. We also obtain refinements controlling the ordinals and hyperjumps of the selected subsets.
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BibTeX
@misc{cintioli2026every,
title = {{Every introenumerable set contains a uniformly introreducible subset}},
author = {Patrizio Cintioli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17605},
eprint = {2609.17605},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17605},
}
RIS
TY - UNPB
TI - Every introenumerable set contains a uniformly introreducible subset
AU - Patrizio Cintioli
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.17605
UR - https://arxiv.org/abs/2609.17605
AB - We prove that every infinite introenumerable set contains an infinite uniformly introreducible subset, answering both parts of Question 1.7 of Greenberg, Harrison-Trainor, Patey, and Turetsky affirmatively. Moreover, a single procedure computes the original set from every infinite subset of the selected set. The proof combines the uniformization and refinement results of these authors with Ramsey-theoretic methods and a canonical reconstruction argument. We also obtain refinements controlling the ordinals and hyperjumps of the selected subsets.
ER -