first incompleteness theorem
GPTKB entity
Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Gödel's_first_incompleteness_theorem
|
| gptkbp:appliesTo |
gptkb:Zermelo–Fraenkel_set_theory
gptkb:Peano_arithmetic |
| gptkbp:countryOfPublication |
gptkb:German
|
| gptkbp:field |
gptkb:logic
metamathematics |
| gptkbp:formedBy |
gptkb:Kurt_Gödel
1931 |
| gptkbp:hasConcept |
formal systems
undecidability incompleteness |
| https://www.w3.org/2000/01/rdf-schema#label |
first incompleteness theorem
|
| gptkbp:influenced |
gptkb:logic
computer science foundations of mathematics |
| gptkbp:publishedIn |
gptkb:Über_formal_unentscheidbare_Sätze_der_Principia_Mathematica_und_verwandter_Systeme_I
|
| gptkbp:relatedTo |
gptkb:second_incompleteness_theorem
|
| gptkbp:state |
Any consistent formal system that is sufficiently expressive to encode arithmetic contains true statements that cannot be proven within the system.
|
| gptkbp:bfsParent |
gptkb:An_Unsolvable_Problem_of_Elementary_Number_Theory
|
| gptkbp:bfsLayer |
6
|