Friedman--Stanley cofinality without Borel completeness

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.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-03
DOI
https://doi.org/10.48550/arxiv.2611.04172
Primary Topic
Advanced Topology and Set Theory
Type
preprint
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preprint

Friedman--Stanley cofinality without Borel completeness

Ruijun Wang
arXiv (Cornell University)
Advanced Topology and Set Theory
preprint

Friedman--Stanley cofinality without Borel completeness

Ruijun Wang
preprint en

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.

arXiv (Cornell University)
Advanced Topology and Set Theory
DOIOpen Access PDFOpenAlex
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Friedman--Stanley cofinality without Borel completeness — Ruijun Wang · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS