Gödel's Incompleteness Theorems
GPTKB entity
Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
arithmetic
formal axiomatic systems |
| gptkbp:citation |
many mathematical and philosophical works
|
| gptkbp:consistsOf |
gptkb:First_Incompleteness_Theorem
gptkb:Second_Incompleteness_Theorem |
| gptkbp:field |
gptkb:logic
metamathematics |
| gptkbp:firstTheoremStates |
Any consistent formal system that is sufficiently expressive cannot be complete.
|
| gptkbp:formedBy |
gptkb:Kurt_Gödel
|
| gptkbp:impact |
foundations of mathematics
|
| gptkbp:influenced |
gptkb:Alan_Turing
gptkb:logic computability theory |
| gptkbp:language |
gptkb:German
|
| gptkbp:publishedIn |
gptkb:Monatshefte_für_Mathematik
|
| gptkbp:relatedTo |
gptkb:Hilbert's_program
gptkb:Peano_arithmetic completeness undecidability consistency |
| gptkbp:secondTheoremStates |
No consistent system can prove its own consistency.
|
| gptkbp:year |
1931
|
| gptkbp:bfsParent |
gptkb:Collected_Works_of_Kurt_Gödel
|
| gptkbp:bfsLayer |
6
|
| https://www.w3.org/2000/01/rdf-schema#label |
Gödel's Incompleteness Theorems
|