Add Erdős Problem 1168 (ℵ_{ω+1} partition without GCH)#3792
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henrykmichalewski wants to merge 4 commits into
Open
Add Erdős Problem 1168 (ℵ_{ω+1} partition without GCH)#3792henrykmichalewski wants to merge 4 commits into
henrykmichalewski wants to merge 4 commits into
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Mirrors the Round C docstring pass from the private repo's phase1-infrastructure branch. Each Lean file now carries the canonical source statement and upstream URL inline so reviewers can verify formalization against the source without navigating away from the diff.
Paul-Lez
reviewed
May 7, 2026
| **Status**: OPEN. | ||
| -/ | ||
| @[category research open, AMS 5] | ||
| theorem erdos_1168 : CardinalCountableColorRamsey (ℵ_ (ω + 1)) := by |
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Does the source ask to prove the negative partition relation ℵ_{ω+1} ↛ ... without GCH? The quoted text has \not\to, but this theorem states the positive CardinalCountableColorRamsey. Could you negate the relation here, or rename this as the positive predicate and make the main theorem ¬ CardinalCountableColorRamsey ...?
Paul-Lez
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Per Paul-Lez's review, the source asserts the NOT-arrow
$\aleph_{\omega+1}\not\to(\aleph_{\omega+1},3,…)^2_{\aleph_0}$, but the
headline previously stated the positive `CardinalCountableColorRamsey`.
Negate it (and the matching `under_GCH` known-result variant for
consistency).
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Thanks for the review @PaulLez. Pushed 82bfdfd on |
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Formalizes Erdős Problem 1168 on a partition relation for
ℵ_{ω+1}that does not assume GCH.Contents
CardinalCountableColorRamsey κ: generalizes the partition statement toℵ_0colors.under_GCHvariant relating the statement to its form under the Generalized Continuum Hypothesis.Closes #1992
Assisted by Claude (Anthropic).