In this note we show that ω1-Universally Baire selfjustifying systems are fully Universally Baire under the Weak Stationary Reflection Principle for Pairs. This involves analyzing the notion of a… (More)

We study a strengthening of Bounded Martin’s Maximum which asserts that if a Σ1 fact holds of ω V 2 in a stationary set preserving extension then it holds in V for a stationary set of ordinals less… (More)

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… (More)

We study reflection principles involving nonmeager sets and the Baire Property which are consequences of the generic supercompactness of ω2, such as the principle asserting that any point countable… (More)