Forcing Axioms, the Uniformization and the Basis Property

2020/01/22 by Hoffelner, Stefan · 3 citations
#03E15 #03E35 #03E45 #03E57 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2001.07977

Abstract

We show that there are models of MA where the boldface Σ¹₃-uniformization property holds. Further we show that BPFA and the assertion ℵ₁ is accessible to reals outright implies that the boldface Σ¹₃-uniformization property is true.

Cited by

• Forcing upper Σ-uniformization in the presence of lower Π-reduction or uniformization
• MA (I) and a Failure of Separation on the third Level
• A Universe with large Continuum, global Σ-Uniformization and a projective Well-Order of its Reals

Related

• The global Σ¹_n+1-Uniformization Property and BPFA
• Forcing the Π¹_n-Uniformization Property
• Forcing the Π¹₃-Reduction Property and a Failure of Π¹₃-Uniformization
• Forcing upper Σ-uniformization in the presence of lower Π-reduction or uniformization
• MA_ω1(S)[S] does not imply K₂