Exercise · ZW-GODELS-INCOMPLETENESS-004 · ★☆☆ Basic
To apply the idea of incompleteness, the system must be able to express at least...
Choose one option.
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- A. Elementary arithmetic
Explanation
To express self-reference, the system needs at least elementary arithmetic. That is why it is the key requirement.
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-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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