Gödel's second incompleteness theorem
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Zermelo–Fraenkel_set_theory
first-order arithmetic sufficiently strong formal systems |
| gptkbp:consequence |
no proof of consistency from within the system
|
| gptkbp:countryOfPublication |
gptkb:German
|
| gptkbp:field |
gptkb:logic
metamathematics |
| gptkbp:formedBy |
gptkb:Kurt_Gödel
1931 |
| https://www.w3.org/2000/01/rdf-schema#label |
Gödel's second incompleteness theorem
|
| gptkbp:impact |
demonstrated limits of formal systems
|
| gptkbp:influenced |
gptkb:Hilbert's_program
gptkb:logic computer science proof theory |
| gptkbp:publishedIn |
gptkb:Über_formal_unentscheidbare_Sätze_der_Principia_Mathematica_und_verwandter_Systeme_I
|
| gptkbp:relatedTo |
gptkb:Hilbert's_program
gptkb:Peano_arithmetic gptkb:Gödel's_first_incompleteness_theorem |
| gptkbp:state |
No consistent system strong enough to express arithmetic can prove its own consistency
|
| gptkbp:bfsParent |
gptkb:Gödel's_first_incompleteness_theorem
|
| gptkbp:bfsLayer |
7
|