2010/03/31 by Marcin Sabok, Sabok, Marcin
Computer Science · Mathematics · #03E15 #28A05 #54H05 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO) #math.LO #msc:03E15 #msc:28A05 #msc:54H05
paper · pdf · doi:10.48550/arxiv.1003.5983
arxiv created 2010/03/31 · openalex publication_date 2010/03/31 · arxiv updated 2010/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the set of codes for Ramsey positive analytic sets is \mathbfΣ12-complete. This is a one projective-step higher analogue of the Hurewicz theorem saying that the set of codes for uncountable analytic sets is \mathbfΣ11-complete. This shows a close resemblance between the Sacks forcing and the Mathias forcing. In particular, we get that the σ-ideal of Ramsey null sets is not ZFC-correct. This solves a problem posed by Ikegami, Pawlikowski and Zapletal.