A Note on the Decidability of the Necessity of Axioms
Por Camilo Arcaya • 31 ago, 2014 • Sección: LeyesMerlin Carl
Abstract: 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.
arXiv:1408.5314v1 [math.LO]
Logic (math.LO)
