Forcing a mutual stationarity property in cofinality 𝜔₁

Abstract

We show that the consistency strength, relative to the system ZFC \operatorname {ZFC} , of the mutual stationarity property MS ⁡ ( ℵ 3 , ℵ 5 , ℵ 7 , … ; ω 1 ) \operatorname {MS} (\aleph _3,\aleph _5, \aleph _7, \ldots ; \omega _1 ) is equal to the existence of one measurable cardinal. We also discuss mutual stationarity for some other configurations of small cardinal parameters.