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Research questionCan any finite formal system autonomously derive every theorem within its expressive scope?A system may be able to express a theorem without having an autonomous procedure that produces it. The central issue is whether finite formal systems can be complete with respect to the theorems they can express.
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Latest papersRecent research connected to this question, newest first.A Non-Formulable Theorem: A Fundamental Limit of Finite Syntactic Systems and Its Consequences for Security and AIThe source states a metatheorem applying to every coherent and sufficiently expressive finite syntactic system, including security mechanisms, AI systems, formal verifiers, legal systems, economic models, and the formal system in which the result is proved. It provides a theoretical result rather than implementation details or empirical evaluation.research paper · Sep 3, 2026
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