MA (I) and a Failure of Separation on the third Level

2025/07/01 by Hoffelner, Stefan · 1 citation
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2507.01187

Abstract

We present a method which forces the failure of Π¹₃ and Σ¹₃-separation, while MA (I) holds, for I the family of indestructible ccc forcings. This shows that, in contrast to the assumption BPFA and ℵ₁=ℵ₁^L which implies Π¹₃-separation, that weaker forcing axioms do not decide separation on the third projective level.

Citations

• Forcing the Π¹_n-Uniformization Property
• Forcing Axioms, the Uniformization and the Basis Property
• Models of set theory in which separation theorem fails

Cited by

• Forcing upper Σ-uniformization in the presence of lower Π-reduction or uniformization

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