Type of Publication: | Preprint |
Author: | Carl, Merlin |
Year of publication: | 2014 |
ArXiv-ID: | arXiv:1408.5314 |
Summary: |
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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Subject (DDC): | 510 Mathematics |
Keywords: | Mathematics, Logic |
Bibliography of Konstanz: | Yes |
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CARL, Merlin, 2014. A Note on the Decidability of the Necessity of Axioms
@unpublished{Carl2014Decid-29876, title={A Note on the Decidability of the Necessity of Axioms}, year={2014}, author={Carl, Merlin} }
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