Club isomorphisms on higher Aronszajn trees

2017/08/01 by Krueger, John
#03E35 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1708.00528

Abstract

We prove the consistency, assuming an ineffable cardinal, that any two normal countably closed ω₂-Aronszajn trees are club isomorphic. This work generalizes to higher cardinals the property of Abraham-Shelah that any two normal ω₁-Aronszajn trees are club isomorphic, which follows from \textsfPFA. The statement that any two normal countably closed ω₂-Aronszajn trees are club isomorphic implies that there are no ω₂-Suslin trees, so our proof also expands on the method of Laver-Shelah for obtaining the ω₂-Suslin hypothesis.

Related

• A Large Pairwise Far Family of Aronszajn Trees
• The vanishing levels of a tree
• New consequences of PFA(T^*)
• The Special Aronszajn Tree Property
• The Special Aronszajn Tree Property at κ⁺ and \square_{κ, 2}