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
model theory |
gptkbp:generalizes |
gptkb:Skolem
|
https://www.w3.org/2000/01/rdf-schema#label |
Löwenheim–Skolem theorem
|
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:logic
|
gptkbp:bfsLayer |
4
|