A Note on the Decidability of the Necessity of Axioms

Por • 31 ago, 2014 • Sección: Leyes

Merlin 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)

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