Semistationary and stationary reflection

Abstract

We 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 E^λ_ω := { 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.