Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Gödel's_incompleteness_theorem
|
| gptkbp:appliesTo |
gptkb:Arithmetic
Formal axiomatic systems |
| gptkbp:field |
gptkb:logic
|
| gptkbp:formedBy |
gptkb:Kurt_Gödel
1931 |
| gptkbp:hasPart |
gptkb:First_incompleteness_theorem
gptkb:Second_incompleteness_theorem |
| https://www.w3.org/2000/01/rdf-schema#label |
Incompleteness theorem
|
| gptkbp:influenced |
gptkb:logic
Computer science Metamathematics |
| gptkbp:publishedIn |
gptkb:Monatshefte_für_Mathematik
|
| gptkbp:relatedTo |
gptkb:Hilbert's_program
gptkb:Peano_arithmetic Undecidability Completeness Consistency |
| gptkbp:sentence |
Any consistent formal system that is sufficiently expressive cannot be both complete and consistent.
A system cannot demonstrate its own consistency. There are true statements in arithmetic that cannot be proven within the system. |
| gptkbp:bfsParent |
gptkb:Completeness_theorem
|
| gptkbp:bfsLayer |
5
|