Exercise · ZW-GODELS-INCOMPLETENESS-006 · ★★☆ Intermediate
The incompleteness theorems require systems that can express...
Choose one option.
Show answer
- C. Enough arithmetic
Explanation
The theorems require that the system can represent numbers and basic operations, that is, enough arithmetic.
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-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.
← ZW-GODELS-INCOMPLETENESS-005 ZW-GODELS-INCOMPLETENESS-007 →