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Add Erdős Problem 1168 (ℵ_{ω+1} partition without GCH)#3792

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Add Erdős Problem 1168 (ℵ_{ω+1} partition without GCH)#3792
henrykmichalewski wants to merge 2 commits intogoogle-deepmind:mainfrom
henrykmichalewski:add-problem-1168

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Formalizes Erdős Problem 1168 on a partition relation for ℵ_{ω+1} that does not assume GCH.

Contents

  • New definition CardinalCountableColorRamsey κ: generalizes the partition statement to ℵ_0 colors.
  • The main open theorem statement for Problem 1168.
  • An under_GCH variant relating the statement to its form under the Generalized Continuum Hypothesis.
  • Four proved sanity checks verifying expected behavior of the defined relation.

Closes #1992

Assisted by Claude (Anthropic).

@github-actions github-actions Bot added the erdos-problems Erdős Problems label Apr 17, 2026
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.
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Erdős Problem 1168: Partition Relation for ℵ_{ω+1} Without GCH

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