PreprintCC BY 4.0arXiv
Quagmires and large Suslin forests
Abstract
In 1972, Jech asked whether there exists a Suslin (ω1, ω2)-forest in the constructible universe. As reported by Jech, Laver gave a positive answer, but his proof was never published and appears no longer to be available. In 2015, Eskew introduced the combinatorial principle W*κ(λ), a strengthening of Silver's principle, and used it to construct a coherent Suslin $(κ, λ)$-forest. He then asked whether the principle W*κ+(κ++) holds in L for every regular cardinal κ. We give an affirmative answer to Eskew's question, thereby also settling Jech's question.
Related
- Unimodality of Independence Polynomials for Sufficiently Large Forests
- Barrier Log-Concavity of Large Forests
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- Height and contour processes of Crump–Mode–Jagers forests (III): The binary, homogeneous universality class
BibTeX
@misc{notaro2026quagmires,
title = {{Quagmires and large Suslin forests}},
author = {Lorenzo Notaro},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28505},
eprint = {2608.28505},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28505},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quagmires and large Suslin forests
AU - Lorenzo Notaro
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28505
UR - https://arxiv.org/abs/2608.28505
AB - In 1972, Jech asked whether there exists a Suslin (ω_1, ω_2)-forest in the constructible universe. As reported by Jech, Laver gave a positive answer, but his proof was never published and appears no longer to be available. In 2015, Eskew introduced the combinatorial principle W^*_κ(λ), a strengthening of Silver's principle, and used it to construct a coherent Suslin $(κ, λ)$-forest. He then asked whether the principle W^*_κ^+(κ^++) holds in L for every regular cardinal κ. We give an affirmative answer to Eskew's question, thereby also settling Jech's question.
ER -