Gödel's incompleteness theorems (1931)
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:author |
gptkb:Kurt_Gödel
|
| gptkbp:countryOfPublication |
gptkb:German
|
| gptkbp:field |
gptkb:logic
|
| gptkbp:firstTheoremStatement |
Any consistent formal system that is capable of expressing elementary arithmetic cannot be both complete and consistent.
|
| https://www.w3.org/2000/01/rdf-schema#label |
Gödel's incompleteness theorems (1931)
|
| gptkbp:influenced |
gptkb:mathematics
gptkb:philosophy computer science |
| gptkbp:notableFor |
impact on foundations of mathematics
showing limitations of formal axiomatic systems |
| gptkbp:numberOfTheorems |
2
|
| gptkbp:publicationYear |
1931
|
| gptkbp:publisher |
gptkb:Über_formal_unentscheidbare_Sätze_der_Principia_Mathematica_und_verwandter_Systeme_I
|
| gptkbp:relatedTo |
gptkb:Hilbert's_program
gptkb:Peano_arithmetic completeness formal systems undecidability consistency |
| gptkbp:secondTheoremStatement |
No consistent system can prove its own consistency.
|
| gptkbp:bfsParent |
gptkb:Hilbert's_program
|
| gptkbp:bfsLayer |
4
|