Quagmires and large Suslin forests

Lorenzo Notaro

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arXiv · 2608.28505

Quagmires and large Suslin forests

Lorenzo Notaro

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Abstract

In 1972, Jech asked whether there exists a Suslin $(\omega_1, \omega_2)$-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 $W^*_\kappa(\lambda)$, a strengthening of Silver's principle, and used it to construct a coherent Suslin $(\kappa, \lambda)$-forest. He then asked whether the principle $W^*_{\kappa^+}(\kappa^{++})$ holds in $\mathsf{L}$ for every regular cardinal $\kappa$. We give an affirmative answer to Eskew's question, thereby also settling Jech's question.

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Lorenzo Notaro. 2026-08-28. Quagmires and large Suslin forests. https://arxiv.org/abs/2608.28505

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