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PreprintCC BY 4.0HAL

Kim-forking for hyperimaginaries in nsop1 theories

  • Yvon Bossut
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Abstract

We adapt the properties of Kim-independence in NSOP1 theories with existence proven in [5],[4] and [2] by Ramsey, Kaplan, Chernikov, Dobrowolski and Kim to hyperimaginaries by adding the assumption of existence for hyperimaginaries. We show that Kim-independence over hyperimaginaries satisfies a version of Kim’s lemma, symmetry, the independence theorem, transitivity and witnessing. As applications we adapt Kim’s results around colinearity and weak canonical bases from [8] to hyperimaginaries and give some new results about Lascar strong types and Kim-forking using boundedly closed hyperimaginaries.

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Cite

BibTeXRIS
BibTeX
@misc{bossut2026kimforking,
  title = {{Kim-forking for hyperimaginaries in nsop1 theories}},
  author = {Yvon Bossut},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  eprint = {2210.14203},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-03823276v4},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Kim-forking for hyperimaginaries in nsop1 theories
AU  - Yvon Bossut
PY  - 2026
DA  - 2026/09/17
PB  - HAL
UR  - https://hal.science/hal-03823276v4
AB  - We adapt the properties of Kim-independence in NSOP1 theories with existence proven in [5],[4] and [2] by Ramsey, Kaplan, Chernikov, Dobrowolski and Kim to hyperimaginaries by adding the assumption of existence for hyperimaginaries. We show that Kim-independence over hyperimaginaries satisfies a version of Kim’s lemma, symmetry, the independence theorem, transitivity and witnessing. As applications we adapt Kim’s results around colinearity and weak canonical bases from [8] to hyperimaginaries and give some new results about Lascar strong types and Kim-forking using boundedly closed hyperimaginaries.
ER  -