Exercise · ZW-GODELS-INCOMPLETENESS-007 · ★★☆ Intermediate
An undecidable sentence is one that...
Choose one option.
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- B. Can be neither proved nor refuted within the system
Explanation
An undecidable sentence is one that the system can neither prove nor refute, even though it is well formed.
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
- ZW-GODELS-INCOMPLETENESS-001 Gödel's incompleteness refers to systems that are...
- ZW-GODELS-INCOMPLETENESS-002 A result of Gödel is that certain systems contain propositions...
- ZW-GODELS-INCOMPLETENESS-003 Gödel's coding relates formulas to...
- ZW-GODELS-INCOMPLETENESS-004 To apply the idea of incompleteness, the system must be able to express at least...
- ZW-GODELS-INCOMPLETENESS-005 Gödel's incompleteness does not claim that...
- ZW-GODELS-INCOMPLETENESS-006 The incompleteness theorems require systems that can express...
- ZW-GODELS-INCOMPLETENESS-008 The first incompleteness theorem states that there is a formula the system cannot...
- ZW-GODELS-INCOMPLETENESS-009 Select the feature associated with Gödel's result.
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