2014/08/22 by Merlin Carl, Carl, Merlin
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Algebra over a field #Axiom #Calculus (dental) #Decidability #Discrete mathematics #Epistemology #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Mathematical economics #Mathematics #Philosophy #Pure mathematics #Statement (logic) #Undecidable problem #math.LO
paper · pdf · doi:10.48550/arxiv.1408.5314
arxiv created 2014/08/22 · openalex publication_date 2014/08/22 · arxiv updated 2014/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A typical kind of question in mathematical logic is that for the necessity of a certain axiom: Given a proof of some statement ϕ in some axiomatic system T, one looks for minimal subsystems of T that allow deriving ϕ. In particular, one asks whether, given some system T+ψ, T alone suffices to prove ϕ. We show that this problem is undecidable unless T+¬ψ is decidable.