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arXiv · 2610.05611

Recovering a structure from its tree of tuples

David Gonzalez·Matthew Harrison-Trainor·Julia Knight
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Abstract

We show that for each countable ordinal $α$, there is a $\mathbfΔ^0_α$ operator that, for all $A$ of Scott rank at most $α$, takes copies of $T_A$ to copies of $A$, where $T_A$ is the tree of tuples corresponding to $A$. For finite $α$, we show that this is best possible. The proof that there is a $\mathbfΔ^0_α$ operator uses Harrington's method of workers. The sharpness result, for finite $n$, uses recent work of Harrison-Trainor on ``unfriendly jump inversion.''

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David Gonzalez, Matthew Harrison-Trainor, Julia Knight. 2026-10-04. Recovering a structure from its tree of tuples. https://arxiv.org/abs/2610.05611

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