The Consistency of the \bfΣ¹₃-Separation Property

2019/12/26 by Stefan Hoffelner, Hoffelner, Stefan
Computer Science · Mathematics · #03E15 #03E35 #03E45 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1912.11811

openalex publication_date 2019/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generically construct a model in which the \bfΣ¹₃-separation property is true, i.e. every pair of disjoint \bfΣ¹₃-sets can be separated by a \bfΔ¹₃-definable set. This answers an old question from the problem list "Surrealist landscape with figures" by A. Mathias from 1968. We also construct a model in which the (lightface) Σ¹₃-separation property is true.

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