Aronszajn trees and maximality

Omer Ben-Neria; Siiri Kivimäki; Menachem Magidor; Jouko Väänänen

Aronszajn trees and maximality

Logic 2025-12-05 v2

Authors: Omer Ben-Neria , Siiri Kivimäki , Menachem Magidor , Jouko Väänänen

Abstract

Assuming the consistency of a weakly compact cardinal above a regular uncountable cardinal $\mu$ , we prove the consistency of the existence of a wide $\mu^+$ -Aronszajn tree, i.e. a tree of height and cardinality $\mu^+$ with no branches of length $\mu^+$ , into which every wide $\mu^+$ -Aronszajn tree can be embedded.

Keywords

trees

Cite

@article{arxiv.2305.07880,
  title  = {Aronszajn trees and maximality},
  author = {Omer Ben-Neria and Siiri Kivimäki and Menachem Magidor and Jouko Väänänen},
  journal= {arXiv preprint arXiv:2305.07880},
  year   = {2025}
}

Aronszajn trees and maximality

Abstract

Keywords

Cite

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