Semistationary and stationary reflection

Abstract

AbstractWe study the relationship between the semistationary reflection principle and stationary reflection principles. We show that for all regular cardinals λ ≥ ω2 the semistationary reflection principle in the space [λ]ω implies that every stationary subset of ≔ {α ∈ λ ∣ cf(α) = ω} reflects. We also show that for all cardinals λ ≥ ω3 the semistationary reflection principle in [λ]ω does not imply the stationary reflection principle in [λ]ω.