# Mathematical logic

> 6 AI-made results in mathematical logic, each explained in plain English with its trust label, Lean status and sources.

Canonical: https://closedform.nishachay.tech/science/mathematics/mathematical-logic/
Last updated: 2026-10-14

6 results in OpenAI Math 2026.

6 AI-made results in mathematical logic, from 8 papers in the OpenAI math collection, each explained in plain English. All of them have a formal Lean proof listed. The oldest question here dates back to 1965: [Shelah's eventual categoricity and the prescribed-threshold obstruction](https://closedform.nishachay.tech/e/openai-math-2026-240/).

## Results (6)

- [Shelah's eventual categoricity and the prescribed-threshold obstruction](https://closedform.nishachay.tech/e/openai-math-2026-240/) - Entry 240 · Claims Shelah's eventual categoricity conjecture in ZFC, and shows under CH that its proposed exact threshold fails. (Formal proof listed)
- [Rigidity of the Turing degrees](https://closedform.nishachay.tech/e/openai-math-2026-241/) - Entry 241 · Claims every symmetry of the Turing degrees is trivial, settling the rigidity question. (Formal proof listed)
- [Single-fold Diophantine representations and undecidability under an at-most-one-solution promise](https://closedform.nishachay.tech/e/openai-math-2026-242/) - Entry 242 · Every computably listable set gets a whole-number polynomial test with exactly one solution per member. (Formal proof listed)
- [Separating choiceless counting from polynomial time and witnessed choice](https://closedform.nishachay.tech/e/openai-math-2026-243/) - Entry 243 · Claims a polynomial-time query that choiceless polynomial time with counting cannot express. (Formal proof listed)
- [The Partition Principle does not imply Choice](https://closedform.nishachay.tech/e/openai-math-2026-244/) - Entry 244 · Fitting sets back inside their images does not give you the Axiom of Choice. (Formal proof listed)
- [Weak normalization implies strong normalization in pure type systems](https://closedform.nishachay.tech/e/openai-math-2026-245/) - Entry 245 · Claims that in every pure type system, if every legal term can finish computing, then every way of computing finishes. (Formal proof listed)

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