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arXiv · 2609.17605

Every introenumerable set contains a uniformly introreducible subset

Patrizio Cintioli
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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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Patrizio Cintioli. 2026-09-13. Every introenumerable set contains a uniformly introreducible subset. https://arxiv.org/abs/2609.17605

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