Adding cofinal countable sequences through multiple regular cardinals by ssp forcing

Ben De Bondt; Boban Velickovic

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arXiv · 2510.24634

Adding cofinal countable sequences through multiple regular cardinals by ssp forcing

Ben De Bondt·Boban Velickovic

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Abstract

We present a direct construction of stationary set preserving forcings that make $\omega$-cofinal all the members of some arbitrary set $\mathcal{K}$ of regular cardinals $\kappa > \omega_1$. In addition, it is made possible to ensure that no other uncountable regular cardinals from the ground model acquire countable cofinality in the forcing extension. Our method is elementary, being based on a combinatorial argument by Foreman and Magidor together with generalizations of typical side-condition arguments and needs no assumptions beyond $\mathsf{ZFC}$.

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BibTeX RIS

Ben De Bondt, Boban Velickovic. 2025-10-28. Adding cofinal countable sequences through multiple regular cardinals by ssp forcing. https://arxiv.org/abs/2510.24634

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