Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Peano_arithmetic
formal systems |
| gptkbp:concerns |
self-reference
provability predicate |
| gptkbp:consequence |
no consistent system can prove its own consistency
|
| gptkbp:field |
gptkb:logic
provability logic |
| https://www.w3.org/2000/01/rdf-schema#label |
Löb's theorem
|
| gptkbp:namedAfter |
gptkb:Martin_Hugo_Löb
|
| gptkbp:publicationYear |
1955
|
| gptkbp:publishedIn |
gptkb:Journal_of_Symbolic_Logic
|
| gptkbp:relatedTo |
gptkb:Gödel's_incompleteness_theorems
gptkb:logic gptkb:Gödel–Löb_provability_logic |
| gptkbp:sentence |
If a formal system proves that 'if P is provable, then P', then it proves P.
|
| gptkbp:statedIn |
1955
|
| gptkbp:usedIn |
gptkb:logic
proof theory |
| gptkbp:bfsParent |
gptkb:Martin_Löb
|
| gptkbp:bfsLayer |
6
|