A remark on Schimmerling’s question

Joint work with Ari Meir Brodsky.

Abstract. Schimmerling asked whether ${\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.0.3/svg/25fb.svg">}}_{\lambda }^{\ast }$ together with GCH entails the existence of a ${\lambda }^{+}$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a non-reflecting stationary subset of $E_{\ne cf(\lambda )}^{{\lambda }^{+}}$.
As a bonus, the outcome ${\lambda }^{+}$-Souslin tree is moreover free.

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Citation information:

A. M. Brodsky and A. Rinot, A remark on Schimmerling’s question, Order, 36(3): 525-561, 2019.