Models of set theory in which separation theorem fails

2019/05/24 by Kanovei, Vladimir, Lyubetsky, Vassily · 2 citations
#03E15 #03E35 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1905.11241

Abstract

We make use of a finite support product of the Jensen minimal forcing to define a model of set theory in which the separation theorem fails for projective classes \mathbfΣ¹_n and \mathbfΠ¹_n, for a given n≥3.

Cited by

• Notes on the equiconsistency of ZFC without the Power Set axiom and second order PA
• MA (I) and a Failure of Separation on the third Level

Related

• On Harrington's model in which Separation holds but Reduction fails at the 3rd projective level, and on some related models of Sami
• The Consistency of the \bfΣ¹₃-Separation Property
• MA (I) and a Failure of Separation on the third Level
• A Failure of Π¹_n+3-Reduction in the Presence of Σ¹_n+3-Separation
• Half of an inseparable pair