Exercise · ZW-GODELS-INCOMPLETENESS-009 · ★☆☆ Basic
Select the feature associated with Gödel's result.
Choose one option.
Show answer
- D. Sufficiently expressive formal systems
Explanation
The result requires sufficiently expressive formal systems. The other options are neither hypotheses nor features of the theorem.
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.
\[\\exists\\varphi\\,(\\mathcal{S}\\nvdash\\varphi\\land\\mathcal{S}\\nvdash\\neg\\varphi)\]
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