PreprintCC BY 4.0arXiv
Friedman--Stanley cofinality without Borel completeness
Abstract
Friedman and Stanley asked whether an invariant Borel class of countable structures must be Borel complete whenever every countable level of their hierarchy reduces to it. We construct a counterexample in one fixed countable language. The structural counterexample and its principal supporting results have been formalized in Lean~4 and it is available on github.
Related
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- A proof of the Stanley-Stembridge conjecture
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- Typical growth of the Füredi-Hajnal and Stanley-Wilf limits
BibTeX
@misc{wang2026friedmanstanley,
title = {{Friedman--Stanley cofinality without Borel completeness}},
author = {Ruijun Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04172},
eprint = {2611.04172},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04172},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Friedman--Stanley cofinality without Borel completeness
AU - Ruijun Wang
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04172
UR - https://arxiv.org/abs/2611.04172
AB - Friedman and Stanley asked whether an invariant Borel class of countable structures must be Borel complete whenever every countable level of their hierarchy reduces to it. We construct a counterexample in one fixed countable language. The structural counterexample and its principal supporting results have been formalized in Lean~4 and it is available on github.
ER -