On a fragment of the universal Baire property for $\Sigma^1_2$ sets
On a fragment of the universal Baire property for $\Sigma^1_2$ sets
There is a well-known global equivalence between $\Sigma ^1_2$ sets having the universal Baire property, two-step $\Sigma ^1_3$ generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact consistency strength of $\Sigma ^1_2$ sets being $(2^{\omega })^{+}$-cc-universally Baire, which is below …