The Baire and perfect set properties at singulars cardinals
Abstract
We construct a model of ZFC with a singular cardinal $\kappa$ such that every subset of $\kappa$ in $L(V_{\kappa+1})$ has both the $\kappa$-Perfect Set Property and the $\mathcal{\vec{U}}$-Baire Property. This is a higher analogue of Solovay's result for $L(\mathbb{R})$. We obtain this configuration starting with large-cardinal assumptions in the realm of supercompactness, thus improving former theorems by Cramer, Shi and Woodin.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.05973
- arXiv:
- arXiv:2408.05973
- Bibcode:
- 2024arXiv240805973D
- Keywords:
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- Mathematics - Logic