Exercise · ZW-GODELS-INCOMPLETENESS-010 · ★★★ Advanced
The second incompleteness theorem is especially related to...
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- C. The impossibility of proving, within the system, its own consistency under certain hypotheses
Explanation
The second incompleteness theorem concerns consistency: under suitable hypotheses, the system cannot prove its own consistency.
Review the concept: Gödel’s incompleteness
A consistent system \(\mathcal{S}\) that represents enough arithmetic is incomplete: there is a formula \(\varphi\) that it can neither prove nor refute.
\[\\exists\\varphi\\,(\\mathcal{S}\\nvdash\\varphi\\land\\mathcal{S}\\nvdash\\neg\\varphi)\]
More practice problems: gödel’s incompleteness
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