The Baire and perfect set properties at singulars cardinals

2024/08/12 by Dimonte, Vincenzo, Poveda, Alejandro, Thei, Sebastiano · 1 citation
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2408.05973

Abstract

We construct a model of ZFC with a singular cardinal κ such that every subset of κ in L(V_κ+1) has both the κ-Perfect Set Property and the \mathcalU-Baire Property. This is a higher analogue of Solovay's result for L(ℝ). We obtain this configuration starting with large-cardinal assumptions in the realm of supercompactness, thus improving former theorems by Cramer, Shi and Woodin.

Cited by

• Combinatorics in Higher Solovay Models

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