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Add Erdős Problem 1173 (set mappings on ω_{ω+1} under GCH)#3794

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Add Erdős Problem 1173 (set mappings on ω_{ω+1} under GCH)#3794
henrykmichalewski wants to merge 2 commits intogoogle-deepmind:mainfrom
henrykmichalewski:add-problem-1173

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Formalizes Erdős Problem 1173 on set mappings and free sets on ω_{ω+1} under GCH.

Contents

  • New IsSetMapping definition (a set mapping f : α → Set α with x ∉ f x and a size bound).
  • New IsFreeSet definition (a subset pairwise disjoint from the mapping's images).
  • The main open theorem statement for Problem 1173.
  • Two proved auxiliary lemmas:
    • monotonicity of IsSetMapping in the size bound
    • an image-size bound for set mappings

Closes #1996

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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Erdös Problem 1173: Formalize Erdős–Hajnal Free Set (Cardinal Arithmetic)

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