Exercise · ZW-GODELS-INCOMPLETENESS-002 · ★☆☆ Basic
A result of Gödel is that certain systems contain propositions...
Choose one option.
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- C. Neither provable nor refutable within the system
Explanation
Gödel showed that certain systems contain propositions that can be neither proved nor refuted within them. That is the central idea of the first incompleteness 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.
\[\\exists\\varphi\\,(\\mathcal{S}\\nvdash\\varphi\\land\\mathcal{S}\\nvdash\\neg\\varphi)\]
More practice problems: gödel’s incompleteness
- ZW-GODELS-INCOMPLETENESS-001 Gödel's incompleteness refers to systems that are...
- 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-007 An undecidable sentence is one that...
- 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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