English

Consistency of square bracket partition relation

Logic 2026-01-07 v1

Abstract

Characteristic earlier results were of the form CON(20[λ]n,22)(2^{\aleph_0} \to [\lambda]^2_{n, 2}), with 202^{\aleph_0} an ex-large cardinal, in the best case the first weakly Mahlo cardinal. Characteristic new results are CON((20=m)+l[k]n,22)((2^{\aleph_0} = \aleph_m) + \aleph_l \to [\aleph_k]^2_{n, 2}), for suitable k<l<mk < l < m. So we improve in three respects: the continuum may be small (e.g. not a weakly Mahlo), we use no large cardinal, and the cardinals λ\lambda involved are <20 < 2^{\aleph_0} after the forcing.

Keywords

Cite

@article{arxiv.2601.02923,
  title  = {Consistency of square bracket partition relation},
  author = {Saharon Shelah},
  journal= {arXiv preprint arXiv:2601.02923},
  year   = {2026}
}

Comments

14 pages

R2 v1 2026-07-01T08:52:27.990Z