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PreprintarXiv licencearXiv

A true Π01 sentence independence of PA

  • Mohammad Golshani
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Abstract

We give a true Π01 sentence φ which is independent of Peano Arithmetic. Moreover, if ϕ̂ denotes its interpretation on ω as a sentence of set theory, then ϕ̂ is a Π01 sentence independent of ZFC.

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Cite

BibTeXRIS
BibTeX
@misc{golshani2026true,
  title = {{A true $Π^0_1$ sentence independence of PA}},
  author = {Mohammad Golshani},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07321},
  eprint = {2611.07321},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07321},
}
RIS
TY  - UNPB
TI  - A true Π^0_1 sentence independence of PA
AU  - Mohammad Golshani
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07321
UR  - https://arxiv.org/abs/2611.07321
AB  - We give a true Π^0_1 sentence φ which is independent of Peano Arithmetic. Moreover, if ϕ̂ denotes its interpretation on ω as a sentence of set theory, then ϕ̂ is a Π^0_1 sentence independent of ZFC.
ER  -