Open Research Index

Shelah's bound for the Hales–Jewett numbers

Gabriel Dahia

Palomar Registrypalomar/PALOMAR-2026-10-22-000020Oct 22, 2026math.COscore 0

Lean 4 formalization of Shelah's proof of the Hales–Jewett theorem. For k ≥ 1 letters and r colors, every coloring with r colors of the words of length n over k letters has a monochromatic combinatorial line when n is at least the Ackermann function at level 5 and argument 2k + r.

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