On a Fragment of the Universal Baire Property for Sigma¹₂ Sets

2006/03/22 by Zoble, Stuart
#03E45 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.math/0603540

Abstract

There is a well-known global equivalence between Σ¹₂ sets having the Universal Baire property, two-step Σ¹₃ generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact consistency strength of Σ¹₂ sets being (2^ω)⁺-cc Universally Baire, which is below 0^#. In a model obtained, there is a Σ¹₂ set which is weakly ω₂-Universally Baire but not ω₂-Universally Baire.

Related

• Universally Baire sets in 2^κ
• The consistency strength of the perfect set property for universally Baire sets of reals
• The exact strength of generic absoluteness for the universally Baire sets
• The model companions of set theory
• Towards a generic absoluteness theorem for Chang models