A choice-free proof of the Erdős--Dushnik--Miller theorem

@misc{shen2026choicefree,
  title = {{A choice-free proof of the Erdős--Dushnik--Miller theorem}},
  author = {Guozhen Shen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02703},
  eprint = {2609.02703},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02703},
}

TY  - UNPB
TI  - A choice-free proof of the Erdős--Dushnik--Miller theorem
AU  - Guozhen Shen
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.02703
UR  - https://arxiv.org/abs/2609.02703
AB  - The Erdős--Dushnik--Miller theorem states that for every aleph κ, κ→(κ,ω); that is, every coloring c:[κ]^2→2 has either a $0$-homogeneous set of cardinality κ or a $1$-homogeneous set of cardinality ω. In this article, we present a purely combinatorial proof of this theorem in ZF (i.e., Zermelo--Fraenkel set theory without the axiom of choice), avoiding any metamathematical considerations.
ER  -