Specializing Trees with Small Approximations I

2021/01/05 by Mohammadpour, Rahman
#03E35 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2101.01594

Abstract

Assuming \rm PFA, we shall use internally club ω₁-guessing models as side conditions to show that for every tree T of height ω₂ without cofinal branches, there is a proper and ℵ₂-preserving forcing notion with finite conditions which specialises T. Moreover, the forcing has the ω₁-approximation property.

Related

• Specialising Trees With Small Approximations II
• Indestructibility of some compactness principles over models of PFA
• Specializing Aronszajn trees by countable approximations
• Guessing models, trees, and cardinal arithmetic
• Classical Namba forcing can have the weak countable approximation property