google-deepmind / google-deepmind/formal-conjectures

ErdosProblems/1175: `variants.shelah_consistency` asserts the counterexample outright, not its consistency

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ai-audit ai-audit-c90271f0fa misformalization
Dominant language
Lean
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Description

`Erdos1175.erdos_1175.variants.shelah_consistency` asks, via `answer(sorry) ↔ ...`, whether an ℵ₁-chromatic graph all of whose triangle-free subgraphs have chromatic number below ℵ₁ exists in the ambient universe, whereas Shelah's result states only that the existence of such a graph is consistent with ZFC.

https://tadamcz.com/fc-review-results/c90271f0fa/#/f/ErdosProblems/1175

- 1 misformalization
- 2 minor
- trivial proof: bailed out
- fix compiles

Found by a language-model audit of the repository at c90271f0fa. Not reviewed by a human. This issue's title and description were written by a language model as well.

Contributor guide

Open the contributing guide

Research direction

Start at Erdos1175.erdos_1175.variants.shelah_consistency and read the linked review to compare the formal statement with Shelah's consistency result. Adjust the assertion so it represents consistency rather than outright existence, then run the relevant Lean checks; done means the corrected declaration compiles.

Written by the indexing model from the issue text.

Assessment

Domain
tooling
Issue type
Bug
Difficulty
3/5
Estimated time
1-2 days
Activity status
Active
Clarity
Clearly specified
Newbie friendliness
55/100

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