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A Remark on Schimmerling’s Question

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Abstract

Schimmerling asked whether \(\square ^{\ast }_{\lambda }+\mathsf {GCH}\) entails the existence of a λ+-Souslin tree, for a singular cardinal λ. We provide an affirmative answer under the additional assumption that there exists a non-reflecting stationary subset of \({E}^{{\lambda }^{+}}_{{\neq } \text {cf}(\lambda )}\). As a bonus, the outcome λ+-Souslin tree is moreover free.

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Acknowledgments

The first author was supported by the Center for Absorption in Science, Ministry of Aliyah and Integration, State of Israel. The second author was partially supported by the European Research Council (grant agreement ERC-2018-StG 802756) and by the Israel Science Foundation (grant agreement 2066/18). We thank the anonymous referee for a careful reading of this paper and for providing valuable feedback.

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Correspondence to Ari Meir Brodsky.

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Brodsky, A.M., Rinot, A. A Remark on Schimmerling’s Question. Order 36, 525–561 (2019). https://doi.org/10.1007/s11083-019-09482-7

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