PreprintCC BY 4.0arXiv
Recovering a structure from its tree of tuples
Abstract
We show that for each countable ordinal α, there is a Δ0α operator that, for all A of Scott rank at most α, takes copies of TA to copies of A, where TA is the tree of tuples corresponding to A. For finite α, we show that this is best possible. The proof that there is a Δ0α operator uses Harrington's method of workers. The sharpness result, for finite n, uses recent work of Harrison-Trainor on ``unfriendly jump inversion.''
Related
- Recovering complex structure from (n,0)-form with implications for Vafa-Witten equation
- Recovering Collective Structure in Congressional Voting: A Fused Latent Factor and Network Approach
- Quasi-periodic tree sets and structure trees
- Structure-Adaptive Tree Field Integrators
- Coupled Pklt Tuples and Varieties of Pklt Type
BibTeX
@misc{gonzalez2026recovering,
title = {{Recovering a structure from its tree of tuples}},
author = {David Gonzalez and Matthew Harrison-Trainor and Julia Knight},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05611},
eprint = {2610.05611},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05611},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Recovering a structure from its tree of tuples
AU - David Gonzalez
AU - Matthew Harrison-Trainor
AU - Julia Knight
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05611
UR - https://arxiv.org/abs/2610.05611
AB - We show that for each countable ordinal α, there is a Δ^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 Δ^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.''
ER -