Publikation: A Note on the Decidability of the Necessity of Axioms
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2014
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A typical kind of question in mathematical logic is that for the necessity of a certain axiom: Given a proof of some statement $\phi$ in some axiomatic system $T$, one looks for minimal subsystems of $T$ that allow deriving $\phi$. In particular, one asks whether, given some system $T+\psi$, $T$ alone suffices to prove $\phi$. We show that this problem is undecidable unless $T+\neg\psi$ is decidable.
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510 Mathematik
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Mathematics, Logic
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CARL, Merlin, 2014. A Note on the Decidability of the Necessity of AxiomsBibTex
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<dcterms:abstract xml:lang="eng">A typical kind of question in mathematical logic is that for the necessity of a certain axiom: Given a proof of some statement $\phi$ in some axiomatic system $T$, one looks for minimal subsystems of $T$ that allow deriving $\phi$. In particular, one asks whether, given some system $T+\psi$, $T$ alone suffices to prove $\phi$. We show that this problem is undecidable unless $T+\neg\psi$ is decidable.</dcterms:abstract>
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