Reals in the Matet and Willow Models

2025/01/15 by Banerjee, Raiean
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2501.08903

Abstract

In this article, we try to complete the regularity implications between the regularitites of the well-known tree forcing notions at the \boldsymbolΔ¹₂ level of the projective hierarchy. The missing links in this case were the regularities corresponding to Matet and Willow tree Forcings. Some of the techniques yield more general results related to locally countable closed graphs too, which we mention as corollaries.

Related

• Specializing Trees with Small Approximations I
• Preserving levels of projective determinacy by tree forcings
• Regularity Properties on the Generalized Reals
• More on trees and Cohen reals
• Diagram-free approach for convergence of tree-based models in Regularity Structures