
TL;DR
This paper proves the consistency, assuming an ineffable cardinal, that all normal countably closed 2-Aronszajn trees are club isomorphic, extending known results from 1 and relating to the 2-Suslin hypothesis.
Contribution
It generalizes the club isomorphism property from 1 to 2-Aronszajn trees under certain large cardinal assumptions.
Findings
All normal countably closed 2-Aronszajn trees are club isomorphic assuming an ineffable cardinal.
The result implies the nonexistence of 2-Suslin trees.
Extends methods for the 2-Suslin hypothesis to higher cardinals.
Abstract
We prove the consistency, assuming an ineffable cardinal, that any two normal countably closed -Aronszajn trees are club isomorphic. This work generalizes to higher cardinals the property of Abraham-Shelah that any two normal -Aronszajn trees are club isomorphic, which follows from . The statement that any two normal countably closed -Aronszajn trees are club isomorphic implies that there are no -Suslin trees, so our proof also expands on the method of Laver-Shelah for obtaining the -Suslin hypothesis.
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