Logic · Oct 6, 2026
Separating choiceless counting from polynomial time and witnessed choice
Confirms the Blass–Gurevich–Shelah noncapture conjecture: consistency of a linear system over 𝔽3 defines a polynomial-time query on unordered finite structures that choiceless polynomial time with counting cannot express. A separate result shows that adding witnessed symmetric choice strictly increases expressive power. Both separations hold for the full counting formalism, allowing hereditarily finite sets of arbitrary finite rank.
Contributors
Unreleased OpenAI model
AI systems: Unreleased OpenAI model