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PreprintCC BY 4.0arXiv

Baire measurable functions and automorphisms of the truth-table degrees

  • Bjørn Kjos-Hanssen
Open at sourcePDFDOICite

Abstract

We show that if an automorphism π of the truth-table degrees is induced by a Baire measurable function F: 2ω→ 2ω, or merely induced on some comeager set by a continuous function, then π is the identity. The same results hold for the weak truth-table degrees. The argument is an adaptation to truth-table reducibility of OpenAI's recent proof that the Turing degrees are rigid.

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Cite

BibTeXRIS
BibTeX
@misc{kjoshanssen2026baire,
  title = {{Baire measurable functions and automorphisms of the truth-table degrees}},
  author = {Bjørn Kjos-Hanssen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16059},
  eprint = {2610.16059},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16059},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Baire measurable functions and automorphisms of the truth-table degrees
AU  - Bjørn Kjos-Hanssen
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16059
UR  - https://arxiv.org/abs/2610.16059
AB  - We show that if an automorphism π of the truth-table degrees is induced by a Baire measurable function F: 2^ω→ 2^ω, or merely induced on some comeager set by a continuous function, then π is the identity. The same results hold for the weak truth-table degrees. The argument is an adaptation to truth-table reducibility of OpenAI's recent proof that the Turing degrees are rigid.
ER  -