Gödel's incompleteness theorems
GPTKB entity
AI-created image
Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:logic
gptkb:Peano_arithmetic formal systems |
| gptkbp:category |
gptkb:logic
theoretical computer science |
| gptkbp:countryOfPublication |
gptkb:German
|
| gptkbp:firstTheoremStates |
Any consistent formal system that is capable of expressing elementary arithmetic cannot be both complete and consistent.
|
| gptkbp:formedBy |
gptkb:Kurt_Gödel
1931 |
| https://www.w3.org/2000/01/rdf-schema#label |
Gödel's incompleteness theorems
|
| gptkbp:influenced |
gptkb:logic
computer science |
| gptkbp:numberOfTheorems |
2
|
| gptkbp:publishedIn |
gptkb:Über_formal_unentscheidbare_Sätze_der_Principia_Mathematica_und_verwandter_Systeme_I
gptkb:Monatshefte_für_Mathematik |
| gptkbp:relatedTo |
gptkb:Hilbert's_program
gptkb:Turing's_halting_problem completeness undecidability consistency |
| gptkbp:secondTheoremStates |
No consistent system can prove its own consistency.
|
| gptkbp:bfsParent |
gptkb:Hilbert's_program
gptkb:logic |
| gptkbp:bfsLayer |
4
|