The Special Aronszajn Tree Property at κ⁺ and \square_{κ, 2}

2019/01/31 by John Susice, Susice, John
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1902.00108

openalex publication_date 2019/01/31 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We show that for any regular cardinal κ, \square_{κ, 2} is consistent with "all κ⁺-Aronszajn trees are special." By a result of Shelah and Stanley this is optimal in the sense that \square_{κ, 2} may not be strengthened to \square_κ. Using methods of Golshani and Hayut we obtain our consistency result simultaneously for all regular κ.

Related

• The Special Aronszajn Tree Property
• How special is your Aronszajn tree?
• Aronszajn trees and maximality
• Aronszajn trees, square principles, and stationary reflection
• The special Aronszajn tree property at ℵ₂ and GCH