English

Club isomorphisms on higher Aronszajn trees

Logic 2018-06-05 v3

Abstract

We prove the consistency, assuming an ineffable cardinal, that any two normal countably closed ω2\omega_2-Aronszajn trees are club isomorphic. This work generalizes to higher cardinals the property of Abraham-Shelah that any two normal ω1\omega_1-Aronszajn trees are club isomorphic, which follows from PFA\textsf{PFA}. The statement that any two normal countably closed ω2\omega_2-Aronszajn trees are club isomorphic implies that there are no ω2\omega_2-Suslin trees, so our proof also expands on the method of Laver-Shelah for obtaining the ω2\omega_2-Suslin hypothesis.

Cite

@article{arxiv.1708.00528,
  title  = {Club isomorphisms on higher Aronszajn trees},
  author = {John Krueger},
  journal= {arXiv preprint arXiv:1708.00528},
  year   = {2018}
}
R2 v1 2026-06-22T21:04:10.619Z