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PreprintCC BY 4.0arXiv

Failure of the G0-dichotomy for generalized Cantor spaces

  • Matteo Casarosa
  • Philipp Schlicht
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Abstract

Kechris, Solecki and Todorčević's G0-dichotomy characterizes Borel graphs that admit a Borel measurable coloring with countably many colors. We show that the analogue to the G0-dichotomy for generalized Cantor spaces fails at the lowest possible complexity, namely for closed graphs.

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Cite

BibTeXRIS
BibTeX
@misc{casarosa2026failure,
  title = {{Failure of the $G_0$-dichotomy for generalized Cantor spaces}},
  author = {Matteo Casarosa and Philipp Schlicht},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07450},
  eprint = {2609.07450},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07450},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Failure of the G_0-dichotomy for generalized Cantor spaces
AU  - Matteo Casarosa
AU  - Philipp Schlicht
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.07450
UR  - https://arxiv.org/abs/2609.07450
AB  - Kechris, Solecki and Todorčević's G_0-dichotomy characterizes Borel graphs that admit a Borel measurable coloring with countably many colors. We show that the analogue to the G_0-dichotomy for generalized Cantor spaces fails at the lowest possible complexity, namely for closed graphs.
ER  -