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PreprintarXiv licencearXiv

Forcing axioms and the structure theory of Aronszajn trees

  • Justin Tatch Moore
  • Stevo Todorcevic
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Abstract

We study which structural results about Aronszajn trees require the Proper Forcing Axiom and which require only MA(aleph1). In particular, we show that MA(aleph1) is consistent with the existence of 2^aleph1 pairwise non-club-isomorphic coherent A-trees.

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Cite

BibTeXRIS
BibTeX
@misc{moore2026forcing,
  title = {{Forcing axioms and the structure theory of Aronszajn trees}},
  author = {Justin Tatch Moore and Stevo Todorcevic},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05574},
  eprint = {2610.05574},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05574},
}
RIS
TY  - UNPB
TI  - Forcing axioms and the structure theory of Aronszajn trees
AU  - Justin Tatch Moore
AU  - Stevo Todorcevic
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05574
UR  - https://arxiv.org/abs/2610.05574
AB  - We study which structural results about Aronszajn trees require the Proper Forcing Axiom and which require only MA(aleph1). In particular, we show that MA(aleph1) is consistent with the existence of 2^aleph1 pairwise non-club-isomorphic coherent A-trees.
ER  -