Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:first-order_logic
|
| gptkbp:category |
logic theorems
|
| gptkbp:concerns |
cardinality of models
|
| gptkbp:field |
gptkb:logic
gptkb:model_theory |
| gptkbp:generalizes |
gptkb:Skolem
|
| gptkbp:importantFor |
shows limitations of first-order logic
|
| gptkbp:influenced |
development of model theory
|
| gptkbp:language |
first-order language
|
| gptkbp:namedAfter |
gptkb:Thoralf_Skolem
gptkb:Leopold_Löwenheim |
| gptkbp:originallyProvedBy |
gptkb:Leopold_Löwenheim
|
| gptkbp:publicationYear |
1915
|
| gptkbp:relatedConcept |
gptkb:Skolem_paradox
completeness theorem compactness theorem |
| gptkbp:sentence |
If a first-order theory has an infinite model, then it has models of all infinite cardinalities.
|
| gptkbp:variant |
gptkb:downward_Löwenheim–Skolem_theorem
gptkb:upward_Löwenheim–Skolem_theorem |
| gptkbp:bfsParent |
gptkb:Gödel–Löwenheim_theorem
|
| gptkbp:bfsLayer |
5
|
| https://www.w3.org/2000/01/rdf-schema#label |
Löwenheim–Skolem theorem
|