STATIONARY REFLECTION

Bounded Stationary Reflection

We prove that, assuming large cardinals, it is consistent that there are many singular cardinals μ such that every stationary subset of μ+ reflects but there are stationary subsets of μ+ that do not reflect at ordinals of arbitrarily high cofinality. This answers a question raised by Todd Eisworth.

Semistationary and stationary reflection

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] implies that every stationary subset of E ω := {α ∈ λ | cf(α) = ω} reflects. We also show that for all cardinals λ ≥ ω3 the semistationary reflection principle in [λ] does not imply ...

Indestructibility and stationary reflection

If κ < λ are such that κ is a strong cardinal whose strongness is indestructible under κ-strategically closed forcing and λ is weakly compact, then we show that A = {δ < κ | δ is a non-weakly compact Mahlo cardinal which reflects stationary sets} must be unbounded in κ. This phenomenon, however, need not occur in a universe with relatively few large cardinals. In particular, we show how to cons...

Squares, Scales and Stationary Reflection

On reflection of stationary sets

We show that there are stationary subsets of uncountable spaces which