On a Fragment of the Universal Baire Property for Σ2 Sets
نویسنده
چکیده
There is a well-known global equivalence between Σ2 sets having the Universal Baire property, two-step Σ3 generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact consistency strength of Σ2 sets being (2 )-cc Universally Baire, which is below 0. In a model obtained, there is a Σ2 set which is weakly ω2-Universally Baire but not ω2-Universally Baire.
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