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Published online by Cambridge University Press: 07 June 2024
This chapter presents a proof $\square_{\kappa,2}$ holds in a lsa-small hod mouse $\mathcal{P}$ for all cardinals $\kappa$ of $\mathcal{P}$. The proof adapts a well-known construction of $\square$ in extender models by Schimmerling-Zeman. The main challenge to overcome in this situation is that the full condensation lemma, which holds for extender models, does not hold in hod mice. The main application of this result is in the proof of consistency of LSA in Chapter 12.
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