2024/04/23 by Jakob, Hannes, Levine, Maxwell
#03E35 #03E55 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2404.15230
Krueger showed that PFA implies that for all regular Θ≥ ℵ2, there are stationarily many [H(Θ)]ℵ1 that are internally club but not internally approachable. From countably many Mahlo cardinals, we force a model in which, for all positive n<ω and Θ≥ ℵn+1, there is a stationary subset of [H(Θ)]ℵn consisting of sets that are internally club but not internally approachable. The theorem is obtained using a new variant of Mitchell forcing. This answers questions of Krueger.